An improved variational iteration method for solving coupled KdV and Boussinesq-like B(m, n) equations

Abstract In this article, we implement a new analytical technique; He’s variational iteration method for solving the coupled KdV and Boussinesq-like equations. In this method, first general Lagrange multipliers are introduced to construct correction functional for the problems. The multipliers in the functional can be identified optimally via the variational theory. Next the components of obtained iteration formulae defined by partial sum of other sequence, specially constructed according to Adomian’s decomposition method (ADM). Also according to ADM we used a partial sum of Adomian polynomials instead of nonlinear terms in iteration formulae. The initial approximations can be freely chosen with possible unknown constants, which can be determined by imposing the initial conditions. The results reveal that the proposed method is very effective and can be applied for other nonlinear problems.

[1]  M. A. Abdou,et al.  Nonlinear fluid flows in pipe-like domain problem using variational-iteration method , 2007 .

[2]  M. A. Abdou,et al.  The solution of nonlinear coagulation problem with mass loss , 2006 .

[3]  M. A. Abdou,et al.  Adomian decomposition method for solving the diffusion-convection-reaction equations , 2006, Appl. Math. Comput..

[4]  Ji-Huan He,et al.  Addendum:. New Interpretation of Homotopy Perturbation Method , 2006 .

[5]  Mehdi Dehghan,et al.  Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices , 2006, Math. Comput. Simul..

[6]  M. A. Abdou,et al.  New applications of Adomian decomposition method , 2007 .

[7]  Ji-Huan He,et al.  Variational iteration method for autonomous ordinary differential systems , 2000, Appl. Math. Comput..

[8]  S. Momani,et al.  Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .

[9]  Q. Chang,et al.  Exact solitary solutions with compact support for the nonlinear dispersive Boussinesq-like B(m,n) equations , 2005 .

[10]  M. A. Abdou,et al.  New application of Adomian decomposition method on Fokker-Planck equation , 2006, Appl. Math. Comput..

[11]  Ji-Huan He,et al.  Construction of solitary solution and compacton-like solution by variational iteration method , 2006 .

[12]  E. Yusufoglu,et al.  Variational Iteration Method for Construction of Some Compact and Noncompact Structures of Klein-Gordon Equations , 2007 .

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

[14]  V. Marinca,et al.  An Approximate Solution for One-Dimensional Weakly Nonlinear Oscillations , 2002 .

[15]  Davood Domiri Ganji,et al.  Approximate Solutions of Κ (2,2), KdV and Modified KdV Equations by Variational Iteration Method, Homotopy Perturbation Method and Homotopy Analysis Method , 2007 .

[16]  Ji-Huan He.  SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[17]  Ji-Huan He,et al.  Application of Parameter-expanding Method to Strongly Nonlinear Oscillators , 2007 .

[18]  M. A. Abdou,et al.  Decomposition method for solving a system of coupled fractional-time nonlinear equations , 2006 .

[19]  Ji-Huan He.  Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[20]  A. A. Soliman,et al.  Variational iteration method for solving Burger's and coupled Burger's equations , 2005 .

[21]  M. A. Abdou.  On the variational iteration method , 2007 .

[22]  Necdet Bildik,et al.  The Use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations , 2006 .

[23]  A. A. Soliman,et al.  New applications of variational iteration method , 2005 .