Single and multi-solitary wave solutions to a class of nonlinear evolution equations

In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate...

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Vydáno v:	Journal of mathematical analysis and applications Ročník 343; číslo 1; s. 273 - 298
Hlavní autoři:	Wang, Deng-Shan, Li, Hongbo
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier Inc 01.07.2008 Elsevier
Témata:	Bessel functions Elliptic equation Exact sciences and technology Factorization technique Global analysis, analysis on manifolds Hirota's bilinear method Mathematical analysis Mathematics Multi-solitary wave Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Painlevé analysis Partial differential equations Riccati equation Sciences and techniques of general use Special functions Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Travelling wave solution Elliptic equation Factorization technique Hirota's bilinear method Painlevé analysis Riccati equation Travelling wave solution Multi-solitary wave Bessel functions Wave equation Bessel function Solitary wave Evolution equation Nonlinear problems Camassa Holm equation Travelling wave Algorithm Non linear equation Direct method Algorithm performance Mathematical analysis Application Non linear wave
ISSN:	0022-247X, 1096-0813
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Abstract	In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa–Holm equation, Kolmogorov–Petrovskii–Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the ( 2 + 1 ) -dimensional asymmetric version of the Nizhnik–Novikov–Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems.
AbstractList	In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa–Holm equation, Kolmogorov–Petrovskii–Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the ( 2 + 1 ) -dimensional asymmetric version of the Nizhnik–Novikov–Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems.
Author	Li, Hongbo Wang, Deng-Shan
Author_xml	– sequence: 1 givenname: Deng-Shan surname: Wang fullname: Wang, Deng-Shan email: wangdsh1980@yahoo.com.cn organization: Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, PR China – sequence: 2 givenname: Hongbo surname: Li fullname: Li, Hongbo organization: Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, PR China
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Cites_doi	10.1002/cpa.10083 10.1103/PhysRevE.72.026616 10.1098/rsta.1981.0178 10.1103/PhysRevE.71.046607 10.1103/PhysRevLett.87.194501 10.1063/1.523393 10.1088/0253-6102/47/2/017 10.1137/0151075 10.1063/1.1598619 10.1103/PhysRevLett.71.1661 10.1088/0305-4470/37/21/012 10.1088/0305-4470/29/13/032 10.1016/j.jde.2004.09.007 10.1016/0167-2789(81)90004-X 10.1016/0020-7462(95)00064-X 10.1088/0305-4470/29/15/026 10.1088/1009-1963/16/7/004 10.1007/s10701-006-9069-5 10.1098/rsta.2007.2009 10.1016/j.jmaa.2004.11.038 10.1103/PhysRevLett.27.1192 10.1063/1.532124 10.1103/PhysRevE.66.046601 10.1088/0266-5611/2/3/005 10.1088/0305-4470/39/37/007 10.1143/PTP.114.533 10.1063/1.525875 10.1016/S0065-2156(08)70254-0 10.1088/0253-6102/45/6/006 10.1098/rsta.1978.0064 10.1088/0305-4470/26/10/001
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Keywords	Elliptic equation Factorization technique Hirota's bilinear method Painlevé analysis Riccati equation Travelling wave solution Multi-solitary wave Bessel functions Wave equation Bessel function Solitary wave Evolution equation Nonlinear problems Camassa Holm equation Travelling wave Algorithm Non linear equation Direct method Algorithm performance Mathematical analysis Application Non linear wave
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References	Fornberg, Whitham (bib016) 1978; 289 Ablowitz, Segur (bib001) 1981 Farlow (bib020) 1982 Fuchssteiner, Fokas (bib011) 1981; 4 Olver, Gudkov (bib015) 1977; 18 Hunter, Saxton (bib024) 1991; 51 Cao, Wang (bib021) 2007; 47 Bona, Pritchard, Scott (bib018) 1981; 302 Boiti, Leon, Manna, Pempinelli (bib025) 1986; 2 Cornejo-Pérez, Negro, Nieto, Rosu, Cornejo-Pérez, Rosu, Rosu, Cornejo-Pérez (bib005) 2006; 36 Estévez, Kuru, Negro, Negro (bib006) 2006; 39 Camassa, Holm, Camassa, Holm, Hyman (bib010) 1993; 71 Vekslerchik (bib026) 2004; 37 Rogers, Schief, Rogers (bib002) 2002 Liu, Liu, Liu (bib004) 2006; 16 Brazhnyi, Konotop (bib014) 2005; 72 Polyanin, Zaitsev (bib023) 1995 Weiss (bib008) 1983; 24 Dullin, Gottwald, Holm (bib012) 2001; 87 Degasperis, Procesi (bib017) 1999 Lenells, Lenells, Lenells (bib027) 2005; 217 Ma, Fuchssteiner (bib009) 1996; 31 McKean (bib013) 2003; 56 Hu, Willox, Hu (bib022) 1996; 29 Tang, Lou, Zhang, Tang, Lou (bib003) 2002; 66 Hirota (bib007) 1971; 27 Isidore (bib019) 1996; 29 Cao (10.1016/j.jmaa.2008.01.039_bib021) 2007; 47 Weiss (10.1016/j.jmaa.2008.01.039_bib008) 1983; 24 McKean (10.1016/j.jmaa.2008.01.039_bib013) 2003; 56 Hunter (10.1016/j.jmaa.2008.01.039_bib024) 1991; 51 Camassa (10.1016/j.jmaa.2008.01.039_bib010_1) 1993; 71 Degasperis (10.1016/j.jmaa.2008.01.039_bib017) 1999 Estévez (10.1016/j.jmaa.2008.01.039_bib006) 2006; 39 Fornberg (10.1016/j.jmaa.2008.01.039_bib016) 1978; 289 Ablowitz (10.1016/j.jmaa.2008.01.039_bib001) 1981 Lenells (10.1016/j.jmaa.2008.01.039_bib027_1) 2005; 217 Rogers (10.1016/j.jmaa.2008.01.039_bib002_1) 2002 Ma (10.1016/j.jmaa.2008.01.039_bib009) 1996; 31 Boiti (10.1016/j.jmaa.2008.01.039_bib025) 1986; 2 Olver (10.1016/j.jmaa.2008.01.039_bib015_1) 1977; 18 Lenells (10.1016/j.jmaa.2008.01.039_bib027_2) 2005; 306 Dullin (10.1016/j.jmaa.2008.01.039_bib012) 2001; 87 Polyanin (10.1016/j.jmaa.2008.01.039_bib023) 1995 Cornejo-Pérez (10.1016/j.jmaa.2008.01.039_bib005_1) 2006; 36 Vekslerchik (10.1016/j.jmaa.2008.01.039_bib026) 2004; 37 Farlow (10.1016/j.jmaa.2008.01.039_bib020) 1982 Hu (10.1016/j.jmaa.2008.01.039_bib022_1) 1996; 29 Tang (10.1016/j.jmaa.2008.01.039_bib003_1) 2002; 66 Lenells (10.1016/j.jmaa.2008.01.039_bib027_3) 2007; 365 Cornejo-Pérez (10.1016/j.jmaa.2008.01.039_bib005_2) 2005; 114 Fuchssteiner (10.1016/j.jmaa.2008.01.039_bib011) 1981; 4 Liu (10.1016/j.jmaa.2008.01.039_bib004_3) 2006; 45 Rogers (10.1016/j.jmaa.2008.01.039_bib002_2) 1990 Brazhnyi (10.1016/j.jmaa.2008.01.039_bib014) 2005; 72 Liu (10.1016/j.jmaa.2008.01.039_bib004_2) 2007; 16 Rosu (10.1016/j.jmaa.2008.01.039_bib005_3) 2005; 71 Gudkov (10.1016/j.jmaa.2008.01.039_bib015_2) 1997; 38 Isidore (10.1016/j.jmaa.2008.01.039_bib019) 1996; 29 Liu (10.1016/j.jmaa.2008.01.039_bib004_1) Camassa (10.1016/j.jmaa.2008.01.039_bib010_2) 1994; 31 Hirota (10.1016/j.jmaa.2008.01.039_bib007) 1971; 27 Hu (10.1016/j.jmaa.2008.01.039_bib022_2) 1993; 26 Tang (10.1016/j.jmaa.2008.01.039_bib003_2) 2003; 44 Bona (10.1016/j.jmaa.2008.01.039_bib018) 1981; 302
References_xml	– volume: 36 start-page: 1587 year: 2006 end-page: 538 ident: bib005 article-title: Travelling-wave solutions for Korteweg–de Vries–Burgers equations through factorizations publication-title: Found. Phys. – volume: 37 start-page: 5667 year: 2004 end-page: 5678 ident: bib026 article-title: Backlund transformations for the Nizhnik–Novikov–Veselov equation publication-title: J. Phys. A: Math. Gen. – year: 1995 ident: bib023 article-title: Exact Solutions for Ordinary Differential Equations – year: 1981 ident: bib001 article-title: Soliton and the Inverse Scattering Transformation – volume: 302 start-page: 457 year: 1981 end-page: 510 ident: bib018 article-title: An evaluation of a model equation for water waves publication-title: Philos. Trans. R. Soc. Lond. Ser. A – volume: 66 start-page: 046601 year: 2002 ident: bib003 article-title: Localized excitations in publication-title: Phys. Rev. E – volume: 2 start-page: 271 year: 1986 end-page: 279 ident: bib025 article-title: On the spectral transform of a Korteweg–de Vries equation in two spatial dimensions publication-title: Inverse Problems – volume: 51 start-page: 1498 year: 1991 ident: bib024 article-title: Dynamics of director fields publication-title: SIAM J. Appl. Math. – volume: 24 start-page: 1405 year: 1983 end-page: 1413 ident: bib008 article-title: The Painlevé property for partial differential equations II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative publication-title: J. Math. Phys. – start-page: 97 year: 2002 end-page: 130 ident: bib002 article-title: Bäcklund and Darboux Transformations Geometry and Modern Applications in Soliton Theory publication-title: Soliton Theory: A Survey of Results – year: 1982 ident: bib020 article-title: Partial Differential Equations for Scientists and Engineers – volume: 39 start-page: 11441 year: 2006 end-page: 11452 ident: bib006 article-title: Travelling wave solutions of two-dimensional Korteweg–de Vries–Burgers and Kadomtsev–Petviashvili equations publication-title: J. Phys. A: Math. Gen. – volume: 29 start-page: 3679 year: 1996 end-page: 3682 ident: bib019 article-title: Exact solutions of a nonlinear dispersive dissipative equation publication-title: J. Phys. A: Math. Gen. – volume: 47 start-page: 270 year: 2007 ident: bib021 article-title: Symbolic computation and publication-title: Commun. Theor. Phys. – volume: 16 start-page: 1832 year: 2006 end-page: 1836 ident: bib004 article-title: Direct integral method, complete discrimination system for polynomial and applications to classifications of all single traveling wave solutions to nonlinear differential equations: A survey publication-title: Chinese J. Phys. – volume: 29 start-page: 4589 year: 1996 end-page: 4592 ident: bib022 article-title: Some new exact solutions of the Novikov–Veselov equation publication-title: J. Phys. A: Math. Gen. – volume: 4 start-page: 47 year: 1981 end-page: 66 ident: bib011 article-title: Symplectic structures, their Backlund transformation and hereditary symmetries publication-title: Phys. D – volume: 217 start-page: 393 year: 2005 end-page: 430 ident: bib027 article-title: Traveling wave solutions of the Camassa–Holm equation publication-title: J. Differential Equations – volume: 289 start-page: 373 year: 1978 end-page: 404 ident: bib016 article-title: A numerical and theoretical study of certain nonlinear wave phenomena publication-title: Philos. Trans. R. Soc. Lond. Ser. A – start-page: 23 year: 1999 end-page: 37 ident: bib017 article-title: Asymptotic integrability publication-title: Symmetry and Perturbation Theory – volume: 71 start-page: 1661 year: 1993 end-page: 1664 ident: bib010 article-title: An integrable shallow water equation with peaked solitons publication-title: Phys. Rev. Lett. – volume: 18 start-page: 1212 year: 1977 end-page: 4803 ident: bib015 article-title: Evolution equations possessing infinitely many symmetries publication-title: J. Math. Phys. – volume: 72 start-page: 026616 year: 2005 ident: bib014 article-title: Stable and unstable vector dark solitons of coupled nonlinear Schrödinger equations: Application to two-component Bose–Einstein condensates publication-title: Phys. Rev. E – volume: 31 start-page: 329 year: 1996 end-page: 338 ident: bib009 article-title: Explicit and exact solutions to a Kolmogorov–Petrovskii–Piskunov equation publication-title: Internat. J. Non-Linear Mech. – volume: 56 start-page: 998 year: 2003 end-page: 1015 ident: bib013 article-title: The Liouville correspondence between the Korteweg–de Vries and the Camassa–Holm hierarchies publication-title: Commun. Pure Appl. Math. – volume: 27 start-page: 1192 year: 1971 ident: bib007 article-title: Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons publication-title: Phys. Rev. Lett. – volume: 87 start-page: 194501 year: 2001 ident: bib012 article-title: An integrable shallow water equation with linear and nonlinear dispersion publication-title: Phys. Rev. Lett. – volume: 56 start-page: 998 year: 2003 ident: 10.1016/j.jmaa.2008.01.039_bib013 article-title: The Liouville correspondence between the Korteweg–de Vries and the Camassa–Holm hierarchies publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.10083 – volume: 72 start-page: 026616 year: 2005 ident: 10.1016/j.jmaa.2008.01.039_bib014 article-title: Stable and unstable vector dark solitons of coupled nonlinear Schrödinger equations: Application to two-component Bose–Einstein condensates publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.72.026616 – volume: 302 start-page: 457 year: 1981 ident: 10.1016/j.jmaa.2008.01.039_bib018 article-title: An evaluation of a model equation for water waves publication-title: Philos. Trans. R. Soc. Lond. Ser. A doi: 10.1098/rsta.1981.0178 – volume: 71 start-page: 046607 year: 2005 ident: 10.1016/j.jmaa.2008.01.039_bib005_3 article-title: Supersymmetric pairing of kinks for polynomial nonlinearities publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.71.046607 – volume: 87 start-page: 194501 year: 2001 ident: 10.1016/j.jmaa.2008.01.039_bib012 article-title: An integrable shallow water equation with linear and nonlinear dispersion publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.87.194501 – volume: 18 start-page: 1212 year: 1977 ident: 10.1016/j.jmaa.2008.01.039_bib015_1 article-title: Evolution equations possessing infinitely many symmetries publication-title: J. Math. Phys. doi: 10.1063/1.523393 – year: 2002 ident: 10.1016/j.jmaa.2008.01.039_bib002_1 – volume: 47 start-page: 270 year: 2007 ident: 10.1016/j.jmaa.2008.01.039_bib021 article-title: Symbolic computation and q-deformed function solutions of (2+1)-dimensional breaking soliton equation publication-title: Commun. Theor. Phys. doi: 10.1088/0253-6102/47/2/017 – volume: 51 start-page: 1498 year: 1991 ident: 10.1016/j.jmaa.2008.01.039_bib024 article-title: Dynamics of director fields publication-title: SIAM J. Appl. Math. doi: 10.1137/0151075 – volume: 44 start-page: 4000 year: 2003 ident: 10.1016/j.jmaa.2008.01.039_bib003_2 article-title: Extended multilinear variable separation approach and multivalued localized excitations for some (2+1)-dimensional integrable systems publication-title: J. Math. Phys. doi: 10.1063/1.1598619 – year: 1995 ident: 10.1016/j.jmaa.2008.01.039_bib023 – start-page: 23 year: 1999 ident: 10.1016/j.jmaa.2008.01.039_bib017 article-title: Asymptotic integrability – volume: 71 start-page: 1661 year: 1993 ident: 10.1016/j.jmaa.2008.01.039_bib010_1 article-title: An integrable shallow water equation with peaked solitons publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.71.1661 – volume: 37 start-page: 5667 year: 2004 ident: 10.1016/j.jmaa.2008.01.039_bib026 article-title: Backlund transformations for the Nizhnik–Novikov–Veselov equation publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/37/21/012 – volume: 29 start-page: 3679 year: 1996 ident: 10.1016/j.jmaa.2008.01.039_bib019 article-title: Exact solutions of a nonlinear dispersive dissipative equation publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/29/13/032 – volume: 217 start-page: 393 year: 2005 ident: 10.1016/j.jmaa.2008.01.039_bib027_1 article-title: Traveling wave solutions of the Camassa–Holm equation publication-title: J. Differential Equations doi: 10.1016/j.jde.2004.09.007 – volume: 4 start-page: 47 year: 1981 ident: 10.1016/j.jmaa.2008.01.039_bib011 article-title: Symplectic structures, their Backlund transformation and hereditary symmetries publication-title: Phys. D doi: 10.1016/0167-2789(81)90004-X – volume: 31 start-page: 329 year: 1996 ident: 10.1016/j.jmaa.2008.01.039_bib009 article-title: Explicit and exact solutions to a Kolmogorov–Petrovskii–Piskunov equation publication-title: Internat. J. Non-Linear Mech. doi: 10.1016/0020-7462(95)00064-X – volume: 29 start-page: 4589 year: 1996 ident: 10.1016/j.jmaa.2008.01.039_bib022_1 article-title: Some new exact solutions of the Novikov–Veselov equation publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/29/15/026 – year: 1981 ident: 10.1016/j.jmaa.2008.01.039_bib001 – start-page: 97 year: 1990 ident: 10.1016/j.jmaa.2008.01.039_bib002_2 article-title: Bäcklund transformations in soliton theory – volume: 16 start-page: 1832 year: 2007 ident: 10.1016/j.jmaa.2008.01.039_bib004_2 article-title: The classification of traveling wave solutions and superposition of multi-solutions to Camassa–Holm equation with dispersion publication-title: Chinese J. Phys. doi: 10.1088/1009-1963/16/7/004 – volume: 36 start-page: 1587 year: 2006 ident: 10.1016/j.jmaa.2008.01.039_bib005_1 article-title: Travelling-wave solutions for Korteweg–de Vries–Burgers equations through factorizations publication-title: Found. Phys. doi: 10.1007/s10701-006-9069-5 – volume: 365 start-page: 2291 year: 2007 ident: 10.1016/j.jmaa.2008.01.039_bib027_3 article-title: Classification of all travelling-wave solutions for some nonlinear dispersive equations publication-title: Philos. Trans. R. Soc. Lond. Ser. A doi: 10.1098/rsta.2007.2009 – volume: 306 start-page: 72 year: 2005 ident: 10.1016/j.jmaa.2008.01.039_bib027_2 article-title: Traveling wave solutions of the Degasperis–Procesi equation publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2004.11.038 – volume: 27 start-page: 1192 year: 1971 ident: 10.1016/j.jmaa.2008.01.039_bib007 article-title: Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.27.1192 – volume: 38 start-page: 4794 issue: 9 year: 1997 ident: 10.1016/j.jmaa.2008.01.039_bib015_2 article-title: A family of exact travelling wave solutions to nonlinear evolution and wave equations publication-title: J. Math. Phys. doi: 10.1063/1.532124 – year: 1982 ident: 10.1016/j.jmaa.2008.01.039_bib020 – volume: 66 start-page: 046601 year: 2002 ident: 10.1016/j.jmaa.2008.01.039_bib003_1 article-title: Localized excitations in (2+1)-dimensional systems publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.66.046601 – volume: 2 start-page: 271 year: 1986 ident: 10.1016/j.jmaa.2008.01.039_bib025 article-title: On the spectral transform of a Korteweg–de Vries equation in two spatial dimensions publication-title: Inverse Problems doi: 10.1088/0266-5611/2/3/005 – volume: 39 start-page: 11441 year: 2006 ident: 10.1016/j.jmaa.2008.01.039_bib006 article-title: Travelling wave solutions of two-dimensional Korteweg–de Vries–Burgers and Kadomtsev–Petviashvili equations publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/39/37/007 – volume: 114 start-page: 533 year: 2005 ident: 10.1016/j.jmaa.2008.01.039_bib005_2 article-title: Nonlinear second order ODEs: Factorizations and particular solutions publication-title: Progr. Theoret. Phys. doi: 10.1143/PTP.114.533 – volume: 24 start-page: 1405 year: 1983 ident: 10.1016/j.jmaa.2008.01.039_bib008 article-title: The Painlevé property for partial differential equations II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative publication-title: J. Math. Phys. doi: 10.1063/1.525875 – volume: 31 start-page: 1 year: 1994 ident: 10.1016/j.jmaa.2008.01.039_bib010_2 article-title: A new integrable shallow water equation publication-title: Adv. Appl. Mech. doi: 10.1016/S0065-2156(08)70254-0 – ident: 10.1016/j.jmaa.2008.01.039_bib004_1 – volume: 45 start-page: 991 year: 2006 ident: 10.1016/j.jmaa.2008.01.039_bib004_3 article-title: All single traveling wave solutions to (3+1)-dimensional Nizhnik–Novikov–Veselov equation publication-title: Commun. Theor. Phys. (Beijing) doi: 10.1088/0253-6102/45/6/006 – volume: 289 start-page: 373 year: 1978 ident: 10.1016/j.jmaa.2008.01.039_bib016 article-title: A numerical and theoretical study of certain nonlinear wave phenomena publication-title: Philos. Trans. R. Soc. Lond. Ser. A doi: 10.1098/rsta.1978.0064 – volume: 26 start-page: L465 year: 1993 ident: 10.1016/j.jmaa.2008.01.039_bib022_2 article-title: Generalized Hirota's bilinear equations and their soliton solutions publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/26/10/001
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Snippet	In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to...
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SubjectTerms	Bessel functions Elliptic equation Exact sciences and technology Factorization technique Global analysis, analysis on manifolds Hirota's bilinear method Mathematical analysis Mathematics Multi-solitary wave Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Painlevé analysis Partial differential equations Riccati equation Sciences and techniques of general use Special functions Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Travelling wave solution
Title	Single and multi-solitary wave solutions to a class of nonlinear evolution equations
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