Based on computerized symbolic computation and a new general ansatz,an extended Riccati equation rational expansion method is presented to construct multiple exact solutions for nonlinear evolution equations and implemented in a computer algebraic system.The validity and reliability of the method are tested by its application to four nonlinear evolution equations arising in physics,namely,gener...

By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional KadomtsevPetviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by whic...

The periodic wave solution for the generalized Hirota-Satsuma system was obtained by using the F-expansion method which can be thought of as a generalization of the Jacobi elliptic function method proposed recently. The Adomian decomposition method is used to solve the same system numerically and the approximate solution is compared with the exact solution. Moreover, we analyze the absolute err...

Geometric interpretation of the Hirota equation is presented as equation describing the Laplace sequence of two-dimensional quadrilateral lattices. Different forms of the equation are given together with their geometric interpretation: (i) the discrete coupled Volterra system for the coefficients of the Laplace equation, (ii) the gauge invariant form of the Hirota equation for projective invari...

In this work we apply an extended hyperbolic function method to solve the nonlinear family of third order Korteweg de-Vries (KdV) equations, namely, the KdV equation, the modified KdV (mKdV) equation, the potential KdV (pKdV) equation, the generalized KdV (gKdV) equation and gKdV with two power nonlinearities equation. New exact travelling wave solutions are obtained for the KdV, mKdV and pKdV ...

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)...

We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant R-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic...

In this paper, we first obtain generalized soliton solutions of the general elliptic and auxiliary equations by the Exp-function method. Then by the obtained solutions, we find new and more general solutions of the coupled KdV equation. AMS Subject Classification : 35C05.

A generalized (G ′ /G)-expansion method is used to search for the exact traveling wave solutions of the coupled KdV-mKdV equation. As a result, some new Jacobi elliptic function solutions are obtained. It is shown that the method is straightforward, concise, effective, and can be used for many other nonlinear evolution equations in mathematical physics.