Numerical complexiton solutions for the complex KdV equation by the homotopy perturbation method

[1]  Yong Chen,et al.  Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives , 2008, Appl. Math. Comput..

[2]  S. Lou,et al.  Special solutions from the variable separation approach: the Davey - Stewartson equation , 1996 .

[3]  Zhenya Yan.  New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations , 2001 .

[4]  Saeid Abbasbandy,et al.  Application of He’s homotopy perturbation method to functional integral equations , 2007 .

[5]  Yong Chen,et al.  A unified rational expansion method to construct a series of explicit exact solutions to nonlinear evolution equations , 2006, Appl. Math. Comput..

[6]  V. Konotop,et al.  Dynamics of matter solitons in weakly modulated optical lattices , 2004, Proceedings of 2004 6th International Conference on Transparent Optical Networks (IEEE Cat. No.04EX804).

[7]  Abdul-Majid Wazwaz,et al.  Partial differential equations : methods and applications , 2002 .

[8]  M. Kruskal,et al.  New similarity reductions of the Boussinesq equation , 1989 .

[9]  Abdul-Majid Wazwaz,et al.  A reliable modification of Adomian decomposition method , 1999, Appl. Math. Comput..

[10]  Xiao-yan Tang,et al.  Coupled KdV equations derived from two-layer fluids , 2005, nlin/0508029.

[11]  Norman J. Zabusky,et al.  Soliton , 2010, Scholarpedia.

[12]  Xiao-yan Tang,et al.  Similarity and conditional similarity reductions of a (2+1)-dimensional KdV equation via a direct method , 2000 .

[13]  Zaid M. Odibat,et al.  A new modification of the homotopy perturbation method for linear and nonlinear operators , 2007, Appl. Math. Comput..

[14]  A. Wazwaz.  A reliable modi ® cation of Adomian decomposition method , 1999 .

[15]  S. Lou,et al.  Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equations , 1994 .

[16]  L. Watson.  Numerical linear algebra aspects of globally convergent homotopy methods , 1986 .

[17]  J. Yorke,et al.  Finding zeroes of maps: homotopy methods that are constructive with probability one , 1978 .

[18]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[19]  Roger H.J. Grimshaw,et al.  Weak and strong interactions between internal solitary waves , 1984 .

[20]  V. Matveev,et al.  Darboux Transformations and Solitons , 1992 .

[21]  G. Adomian.  A review of the decomposition method in applied mathematics , 1988 .

[22]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[23]  Yong Chen,et al.  Auto-Bäcklund transformation and exact solutions for modified nonlinear dispersive mK(m,n) equations , 2003 .

[24]  Zhi-bin Li,et al.  Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple , 2004, Comput. Phys. Commun..

[25]  D Gangi,et al.  APPLICATION OF HES HOMOTOPY-PERTURBATION METHOD TO NONLINEAR COUPLED SYSTEMS OF REACTION-DIFFUSION EQUATIONS , 2006 .

[26]  D. Ganji,et al.  Application of He's Homotopy-perturbation Method to Nonlinear Coupled Systems of Reaction-diffusion Equations , 2006 .

[27]  Biao Li.  EXACT SOLITON SOLUTIONS FOR THE HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION , 2005 .

[28]  Xiao-Yan Tang,et al.  Interactions among periodic waves and solitary waves of the (N + 1)-dimensional sine-Gordon field. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Qi Wang,et al.  Multiple Riccati equations rational expansion method and complexiton solutions of the Whitham-Broer-Kaup equation [rapid communication] , 2005 .

[30]  Wen-Xiu Ma,et al.  Complexiton solutions to the Korteweg–de Vries equation , 2002 .

[31]  S. Liao.  An approximate solution technique not depending on small parameters: A special example , 1995 .

[32]  Chen Yong,et al.  Numerical Solutions of a Class of Nonlinear Evolution Equations with Nonlinear Term of Any Order , 2008 .

[33]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[34]  Ji-Huan He.  Approximate analytical solution for seepage flow with fractional derivatives in porous media , 1998 .

[35]  S. Lou,et al.  Nonsingular positon and complexiton solutions for the coupled KdV system , 2005, nlin/0509018.

[36]  J. Gear.  Strong Interactions between Solitary Waves Belonging to Different Wave Modes , 1985 .

[37]  Tien-Yien Li,et al.  Homotopy method for generalized eigenvalue problems Ax= ΛBx☆ , 1987 .

[38]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[39]  Mingliang Wang,et al.  Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics , 1996 .

[40]  A. Golbabai,et al.  A numerical solution for solving system of Fredholm integral equations by using homotopy perturbation method , 2007, Appl. Math. Comput..

[41]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[42]  Ji-Huan He,et al.  Comparison of homotopy perturbation method and homotopy analysis method , 2004, Appl. Math. Comput..

[43]  V V Konotop,et al.  Stable and unstable vector dark solitons of coupled nonlinear Schrödinger equations: application to two-component Bose-Einstein condensates. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Qi Wang,et al.  Homotopy perturbation method for fractional KdV equation , 2007, Appl. Math. Comput..

[45]  E. Fan,et al.  Extended tanh-function method and its applications to nonlinear equations , 2000 .