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Volume 29, Issue 3
Solitons and Other Solutions for the Generalized KdV–mKdV Equation with Higher-order Nonlinear Terms

Elsayed M. E. Zayed & A. G. Al-Nowehy

DOI: 10.4208/jpde.v29.n3.5

J. Part. Diff. Eq., 29 (2016), pp. 218-245.

Published online: 2016-09

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  • Abstract
The generalized sub-ODEmethod, the rational (G' ⁄ G)-expansionmethod, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential equations (PDEs). Some illustrative equations are investigated by these methods and many hyperbolic, trigonometric and rational function solutions are found. We apply these methods to obtain the exact solutions for the generalized KdV-mKdV (GKdV-mKdV) equation with higher-order nonlinear terms. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare between the results yielding from these methods. Also, a comparison between our new results in this paper and the well-known results are given.
  • Keywords

Generalized sub-ODE method rational (G' ⁄ G)-expansion method exp-function method sine-cosine method generalized KdV-mKdV equation with higher-order nonlinear terms exact solutions solitary wave solutions

  • AMS Subject Headings

35C05, 35K99, 35P05, 35P99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

e.m.e.zayed@hotmail.com (Elsayed M. E. Zayed)

alnowehy2010@yahoo.com (A. G. Al-Nowehy)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-29-218, author = {Zayed , Elsayed M. E. and Al-Nowehy , A. G.}, title = {Solitons and Other Solutions for the Generalized KdV–mKdV Equation with Higher-order Nonlinear Terms}, journal = {Journal of Partial Differential Equations}, year = {2016}, volume = {29}, number = {3}, pages = {218--245}, abstract = { The generalized sub-ODEmethod, the rational (G' ⁄ G)-expansionmethod, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential equations (PDEs). Some illustrative equations are investigated by these methods and many hyperbolic, trigonometric and rational function solutions are found. We apply these methods to obtain the exact solutions for the generalized KdV-mKdV (GKdV-mKdV) equation with higher-order nonlinear terms. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare between the results yielding from these methods. Also, a comparison between our new results in this paper and the well-known results are given.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v29.n3.5}, url = {http://global-sci.org/intro/article_detail/jpde/5090.html} }
TY - JOUR T1 - Solitons and Other Solutions for the Generalized KdV–mKdV Equation with Higher-order Nonlinear Terms AU - Zayed , Elsayed M. E. AU - Al-Nowehy , A. G. JO - Journal of Partial Differential Equations VL - 3 SP - 218 EP - 245 PY - 2016 DA - 2016/09 SN - 29 DO - http://doi.org/10.4208/jpde.v29.n3.5 UR - https://global-sci.org/intro/article_detail/jpde/5090.html KW - Generalized sub-ODE method KW - rational (G' ⁄ G)-expansion method KW - exp-function method KW - sine-cosine method KW - generalized KdV-mKdV equation with higher-order nonlinear terms KW - exact solutions KW - solitary wave solutions AB - The generalized sub-ODEmethod, the rational (G' ⁄ G)-expansionmethod, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential equations (PDEs). Some illustrative equations are investigated by these methods and many hyperbolic, trigonometric and rational function solutions are found. We apply these methods to obtain the exact solutions for the generalized KdV-mKdV (GKdV-mKdV) equation with higher-order nonlinear terms. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare between the results yielding from these methods. Also, a comparison between our new results in this paper and the well-known results are given.
Elsayed M. E. Zayed & A. G. Al-Nowehy. (2019). Solitons and Other Solutions for the Generalized KdV–mKdV Equation with Higher-order Nonlinear Terms. Journal of Partial Differential Equations. 29 (3). 218-245. doi:10.4208/jpde.v29.n3.5
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