New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations
We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic func...
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| Vydané v: | Journal of mathematics (Hidawi) Ročník 2013; číslo 2013; s. 1 - 5 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Cairo, Egypt
Hindawi Puplishing Corporation
01.01.2013
Hindawi Publishing Corporation John Wiley & Sons, Inc Wiley |
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| ISSN: | 2314-4629, 2314-4785 |
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| Abstract | We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE), we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena. |
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| AbstractList | We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE), we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena. |
| Author | Ulusoy, Halime Pandir, Yusuf |
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| Cites_doi | 10.1016/j.mcm.2010.10.005 10.1155/2012/265348 10.1016/j.cnsns.2010.06.011 10.1016/j.physleta.2007.04.017 10.1016/j.cnsns.2010.06.001 10.1016/j.cnsns.2011.10.016 10.1016/j.jfranklin.2010.05.013 10.1016/j.amc.2010.08.015 10.1016/j.camwa.2010.08.060 10.1016/j.amc.2009.12.002 10.1063/1.1666400 10.1016/j.cnsns.2010.09.009 10.1016/j.physleta.2006.04.082 10.1016/j.amc.2010.02.045 10.1007/BF02704491 10.1155/2012/478531 10.1016/j.physleta.2007.10.015 10.1016/j.amc.2011.03.157 10.1016/j.cpc.2009.10.006 10.1016/j.chaos.2004.09.109 |
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| Contributor | Ulusoy, Halime |
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| Copyright | Copyright © 2013 Yusuf Pandir and Halime Ulusoy. Copyright © 2013 Yusuf Pandir and Halime Ulusoy. Yusuf Pandir et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Copyright_xml | – notice: Copyright © 2013 Yusuf Pandir and Halime Ulusoy. – notice: Copyright © 2013 Yusuf Pandir and Halime Ulusoy. Yusuf Pandir et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| DOI | 10.1155/2013/201276 |
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| SubjectTerms | Approximation Exact solutions Functions (mathematics) Hyperbolic functions Mathematical analysis Mathematics Nonlinear differential equations Partial differential equations Transformations (mathematics) |
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| Title | New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations |
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