Homotopy perturbation method for a type of nonlinear coupled equations with parameters derivative

[1]  E. Fan,et al.  Soliton solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation , 2001 .

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

[3]  Saeid Abbasbandy,et al.  Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method , 2006, Appl. Math. Comput..

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

[5]  Ji-Huan He A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[6]  Yong Chen,et al.  Explicit exact solutions for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order , 2003 .

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

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

[9]  T. Hayat,et al.  On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder , 2007 .

[10]  I. Podlubny Fractional differential equations , 1998 .

[11]  Layne T. Watson,et al.  Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms , 1987, TOMS.

[12]  Muhammad Aslam Noor,et al.  New iterative schemes for nonlinear equations , 2007, Appl. Math. Comput..

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

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

[15]  T. Hayat,et al.  Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt , 2007 .

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

[17]  Masha Sosonkina,et al.  Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms , 1997, TOMS.

[18]  Layne T. Watson Probability-one homotopies in computational science , 2002 .

[19]  M. Caputo Linear models of dissipation whose Q is almost frequency independent , 1966 .

[20]  M. El-shahed Application of He's Homotopy Perturbation Method to Volterra's Integro-differential Equation , 2005 .

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

[22]  W. Malfliet Series solution of nonlinear coupled reaction-diffusion equations , 1991 .

[23]  Igor M. Sokolov,et al.  Physics of Fractal Operators , 2003 .

[24]  Prince Abdullah bin Ghazi,et al.  Modified homotopy perturbation method : Application to quadratic Riccati differential equation of fractional order , 2007 .

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

[26]  Ji-Huan He Limit cycle and bifurcation of nonlinear problems , 2005 .

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

[28]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[29]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[30]  A. Wazwaz A new approach to the nonlinear advection problem: an application of the decomposition method , 1995 .

[31]  A. Kazakov,et al.  Generation of squeezed states in the presence of a frequency difference , 1991 .

[32]  M. Caputo Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[33]  Mehdi Dehghan,et al.  The solution of coupled Burgers' equations using Adomian-Pade technique , 2007, Appl. Math. Comput..

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

[35]  Dissipative structures in a soluble non-linear reaction-diffusion system , 1977 .

[36]  Ji-Huan He,et al.  The homotopy perturbation method for nonlinear oscillators with discontinuities , 2004, Appl. Math. Comput..

[37]  Ji-Huan He,et al.  A new iteration method for solving algebraic equations , 2003, Appl. Math. Comput..

[38]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

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

[40]  Zhenya Yan,et al.  The Riccati equation with variable coefficients expansion algorithm to find more exact solutions of nonlinear differential equations , 2003 .

[41]  Dogan Kaya,et al.  Exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation , 2004, Appl. Math. Comput..

[42]  Davood Domiri Ganji,et al.  Explicit Solutions of Helmholtz Equation and Fifth-order KdV Equation using Homotopy Perturbation Method , 2006 .

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

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