Exact solutions for the nonlinear Schrödinger equation with variable coefficients using the generalized extended tanh-function, the sine–cosine and the exp-function methods
In this article we find the exact traveling wave solutions of the generalized nonlinear Schrödinger (GNLS) equation with variable coefficients using three methods via the generalized extended tanh-function method, the sine–cosine method and the exp-function method. The main objective of this article...
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| Published in: | Applied mathematics and computation Vol. 218; no. 5; pp. 2259 - 2268 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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01.11.2011
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | In this article we find the exact traveling wave solutions of the generalized nonlinear Schrödinger (GNLS) equation with variable coefficients using three methods via the generalized extended tanh-function method, the sine–cosine method and the exp-function method. The main objective of this article is to compare the efficiency of these methods by delivering the exact traveling wave solutions of the proposed nonlinear equation. |
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| AbstractList | In this article we find the exact traveling wave solutions of the generalized nonlinear Schrödinger (GNLS) equation with variable coefficients using three methods via the generalized extended tanh-function method, the sine–cosine method and the exp-function method. The main objective of this article is to compare the efficiency of these methods by delivering the exact traveling wave solutions of the proposed nonlinear equation. |
| Author | Abdelaziz, M.A.M. Zayed, E.M.E. |
| Author_xml | – sequence: 1 givenname: E.M.E. surname: Zayed fullname: Zayed, E.M.E. email: e.m.e.zayed@hotmail.com – sequence: 2 givenname: M.A.M. surname: Abdelaziz fullname: Abdelaziz, M.A.M. email: mamabdelaziz@hotmail.com |
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| Keywords | Sine–cosine method The generalized nonlinear Schrödinger equation with variable coefficients Exp-function method Generalized extended tanh-function method Exact solutions |
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| References | Zayed, AbdelRahman (b0020) 2010; 1 El-Wakil, Abdou (b0005) 2007; 31 Yaghobi Moghaddam, Asgari, Yazdani (b0045) 2009; 210 Zhao, Zhi, Zhang (b0105) 2006; 28 Liu, Liu, Zhao (b0100) 2001; 289 Wazwaz (b0050) 2004; 40 Wazwaz (b0015) 2007; 187 Fan (b0010) 2000; 277 Zayed, Abdelaziz (b0025) 2010; 11 Zhang, Li, Wang (b0150) 2009; 39 Zhang (b0080) 2008; 38 He (b0115) 2006; 20 Malfliet, Hereman (b0035) 1996; 54 Zhang, Wang, Wang, Fang (b0110) 2006; 350 Yang, Tao, Austin (b0055) 2010; 216 He, Abdou (b0075) 2007; 34 Fan, Zhang (b0060) 1998; 246 Hirota (b0140) 2004 Fan, Zhang (b0095) 2002; 305 He (b0120) 2005; 6 Zhu (b0085) 2007; 8 He, Wu (b0125) 2006; 29 Parkes (b0155) 2010; 217 Dai, Zhang (b0090) 2006; 27 Hirota (b0135) 1980 Wazwaz (b0040) 2004; 154 Ablowitz, Segur (b0130) 1981 Malfliet (b0030) 1992; 60 He, Wu (b0070) 2006; 30 Wazwaz (b0145) 2010; 1 Wang (b0065) 1996; 213 He (10.1016/j.amc.2011.07.043_b0125) 2006; 29 Wazwaz (10.1016/j.amc.2011.07.043_b0145) 2010; 1 El-Wakil (10.1016/j.amc.2011.07.043_b0005) 2007; 31 Wazwaz (10.1016/j.amc.2011.07.043_b0050) 2004; 40 Zhang (10.1016/j.amc.2011.07.043_b0150) 2009; 39 Liu (10.1016/j.amc.2011.07.043_b0100) 2001; 289 Yaghobi Moghaddam (10.1016/j.amc.2011.07.043_b0045) 2009; 210 Hirota (10.1016/j.amc.2011.07.043_b0140) 2004 Zayed (10.1016/j.amc.2011.07.043_b0020) 2010; 1 Malfliet (10.1016/j.amc.2011.07.043_b0030) 1992; 60 Fan (10.1016/j.amc.2011.07.043_b0060) 1998; 246 Zhao (10.1016/j.amc.2011.07.043_b0105) 2006; 28 Wazwaz (10.1016/j.amc.2011.07.043_b0015) 2007; 187 Zayed (10.1016/j.amc.2011.07.043_b0025) 2010; 11 He (10.1016/j.amc.2011.07.043_b0120) 2005; 6 Parkes (10.1016/j.amc.2011.07.043_b0155) 2010; 217 Zhu (10.1016/j.amc.2011.07.043_b0085) 2007; 8 Hirota (10.1016/j.amc.2011.07.043_b0135) 1980 Wang (10.1016/j.amc.2011.07.043_b0065) 1996; 213 Wazwaz (10.1016/j.amc.2011.07.043_b0040) 2004; 154 Yang (10.1016/j.amc.2011.07.043_b0055) 2010; 216 Malfliet (10.1016/j.amc.2011.07.043_b0035) 1996; 54 He (10.1016/j.amc.2011.07.043_b0075) 2007; 34 Fan (10.1016/j.amc.2011.07.043_b0095) 2002; 305 Fan (10.1016/j.amc.2011.07.043_b0010) 2000; 277 He (10.1016/j.amc.2011.07.043_b0115) 2006; 20 Zhang (10.1016/j.amc.2011.07.043_b0080) 2008; 38 Ablowitz (10.1016/j.amc.2011.07.043_b0130) 1981 He (10.1016/j.amc.2011.07.043_b0070) 2006; 30 Dai (10.1016/j.amc.2011.07.043_b0090) 2006; 27 Zhang (10.1016/j.amc.2011.07.043_b0110) 2006; 350 |
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| Snippet | In this article we find the exact traveling wave solutions of the generalized nonlinear Schrödinger (GNLS) equation with variable coefficients using three... |
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| SubjectTerms | Exact solutions Exp-function method Generalized extended tanh-function method Sine–cosine method The generalized nonlinear Schrödinger equation with variable coefficients |
| Title | Exact solutions for the nonlinear Schrödinger equation with variable coefficients using the generalized extended tanh-function, the sine–cosine and the exp-function methods |
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