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New exact travelling wave solutions of nonlinear evolution equation using a sub-equation. (English) Zbl 1197.35257
Summary: By using new solutions of a subsidiary ordinary differential equation, a direct algebraic method is described to construct the exact travelling wave solutions for nonlinear evolution equation. By this method some nonlinear evolution equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
Full Text: DOI
[1] Wang, M.L., Solitary wave solutions for variant Boussinesq equations, Phys lett A, 199, 169-172, (1995) · Zbl 1020.35528
[2] Parkes, E.J.; Duffy, B.R., An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Comp phys commun, 98, 288-300, (1996) · Zbl 0948.76595
[3] Fan, E.G., Extended tanh-function method and its applications to nonlinear equations, Phys lett A, 277, 212-218, (2000) · Zbl 1167.35331
[4] Liu, S.K.; Fu, Z.T.; Liu, S.D., Jacobi elliptic function expansion method and perrodic wave solutions of nonlinear wave equations, Phys lett A, 289, 69-74, (2001)
[5] Zhou, Y.B.; Wang, M.L.; Wang, Y.M., Periodic wave solutions to a coupled KdV equations with variable coefficients, Phys lett A, 308, 31-36, (2003) · Zbl 1008.35061
[6] Sirendaoreji, S., New exact travelling wave solutions for the Kawahara and modified Kawahara equations, Chaos, solitons & fractals, 19, 147-150, (2004) · Zbl 1068.35141
[7] Yan, Zhenya, Envelope compact and solitary pattern structures for the GNLS(m,n,p,q) equations, Phys lett A, 357, 196-203, (2006) · Zbl 1236.35176
[8] Yomba, Emmanuel, The extended fan’s sub-equation method and its application to kdv – mkdv, BKK and variant Boussinesq equations, Phys lett A, 336, 463-476, (2005) · Zbl 1136.35451
[9] Soliman, A.A.; Abdou, M.A., Exact travelling wave solutions of nonlinear partial differential equations, Chaos, solitons & fractals, 32, 808-815, (2007) · Zbl 1138.35402
[10] Zhang, Huiqun, New exact solutions for the sinh-Gordon equation, Chaos, solitons & fractals, 28, 489-496, (2006) · Zbl 1082.35012
[11] Zhang, Huiqun, New exact travelling wave solutions for some nonlinear evolution equations, Chaos, solitons & fractals, 26, 921-925, (2005) · Zbl 1093.35057
[12] Zhang, Huiqun, New exact Jacobi elliptic function solutions for some nonlinear evolution equations, Chaos, solitons & fractals, 32, 653-660, (2007) · Zbl 1139.35394
[13] Xie, F.D.; Zhang, Y.; Lü, Z.S., Symbolic computation in non-linear evolution equation: application to (3+1)-dimensional kadomtsev – petviashvili equation, Chaos, solitons & fractals, 24, 257-263, (2005) · Zbl 1067.35095
[14] Fu, Z.T.; Liu, S.K.; Liu, S.D.; Zhao, Q., New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Phys lett A, 290, 72-76, (2001) · Zbl 0977.35094
[15] Parkes, E.J.; Duffy, B.R.; Abbott, P.C., The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations, Phys lett A, 295, 280-286, (2002) · Zbl 1052.35143
[16] Wang, Dengshan; Zhang, Hong-Qing, Further improved F-expansion method and new exact solutions of konopelchenko – dubrovsky equation, Chaos, solitons & fractals, 25, 601-610, (2005) · Zbl 1083.35122
[17] Wang, Mingliang; Li, Xiangzheng, Exact solutions to the double sine – gordon equation, Chaos, solitons & fractals, 27, 477-486, (2006) · Zbl 1088.35543
[18] Khuri, S.A., Traveling wave solutions for nonlinear differential equations: a unified ansütze approach, Chaos, solitons & fractals, 32, 252-258, (2007) · Zbl 1137.35422
[19] Roy Chowdhury, A.; Dasgupta, B.; Rao, N.N., Painléve analysis and backlund transformations for coupled generalized schrödinger – boussinesq system, Chaos, solitons & fractals, 9, 1747-1753, (1997) · Zbl 0934.35168
[20] Wu, Y.T.; Geng, X.G.; Hu, X.B.; Zhu, S.M., A generalized hirota – satsuma coupled korteweg – de vires equation and miura transformations, Phys lett A, 255, 259-264, (1999) · Zbl 0935.37029
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