A new iterative technique is employed to solve a system of nonlinear fractional partial differential equations. This new approach requires neither Lagrange multiplier like variational iteration method VIM nor polynomials like Adomian’s decomposition method ADM so that can be more easily and effectively established for solving nonlinear fractional differential equations, and will overcome the li...

We introduce a numerical method for general coupled Korteweg-de Vries systems. The scheme is valid for solving Cauchy problems for arbitrary number of equations with arbitrary constant coefficients. The numerical scheme takes its legality by proving its stability and convergence which gives the conditions and the appropriate choice of the grid sizes. The method is applied to Hirota-Satsuma (HS)...

We introduce a numerical method for general coupled Korteweg-de Vries systems. The scheme is valid for solving Cauchy problems for arbitrary number of equations with arbitrary constant coefficients. The numerical scheme takes its legality by proving its stability and convergence which gives the conditions and the appropriate choice of the grid sizes. The method is applied to Hirota-Satsuma (HS)...

The Hirota bilinear formalism and soliton solutions for a generalized Volterra system is presented. Also, starting from the soliton solutions, we obtain a class of nonsingular rational solutions using the ”long wave limit” procedure of Ablowitz and Satsuma, and appropriate ”gauge” transformations. Their properties are also discussed and it is shown that these solutions interact elastically with...

A coupled KdV system with a free parameter proposed by Nutku and Og̃uz is considered. It is shown that the system passes the WTC’s Painlevé test for arbitrary value of the parameter. A further analysis yields that the parameter can be scaled away and the system can be decoupled. Soliton or integrable equations are those systems which have rich structures, such as infinite number of conservation ...

This paper focuses on the exact soliton solutions of (2+1)-dimensional generalized Hirota–Satsuma–Ito equations with time-dependent linear phase speed. Based Painlevé integrability test this equation, condition is determined. Then general N-soliton are constructed by Hirota bilinear method. Not only expressions and their degenerations, but also spatial structures presented for different choices...