Sokolov Wilson System Research Articles

Nonlocal symmetry and explicit solutions for Drinfel’d-Sokolov-Wilson system

Based on the truncated Painleve method and the Mobius (conformal) invariant form, the nonlocal symmetry for the Drinfel’d-Sokolov-Wilson equation is derived. To use symmetry reductions related with nonlocal symmetry, the nonlocal symmetry is localized to the Lie point symmetry by introducing three dependent variables. Thanks to the localization procedure, many group-invariant solutions of the enlarged systems are constructed with similar reductions.

Q‐symmetry and conditional Q‐symmetries for Drinfel'd–Sokolov–Wilson system

We study in this paper the Q‐symmetry and conditional Q‐symmetries of Drinfel'd–Sokolov–Wilson equations. The solutions which we obtain in this paper take the form of convergent power series with easily computable components. Copyright © 2014 John Wiley & Sons, Ltd.

Exact Solutions and Conservation Laws of the Drinfel’d-Sokolov-Wilson System

We study the Drinfel'd-Sokolov-Wilson system, which was introduced as a model of water waves. Firstly we obtain exact solutions of this system using the(G′/G)-expansion method. In addition to exact solutions we also construct conservation laws for the underlying system using Noether's approach.

Double reductions/analysis of the Drinfeld–Sokolov–Wilson equation

In this paper, we show that the recently developed formulation of the association between symmetries and conservation laws lead to double reductions of the third-order Drinfeld–Sokolov–Wilson system of partial differential equations (PDEs). For illustrative purposes only, we carry out the procedure for a version of the well-known third-order scalar Korteweg–de Vries (KdV) equation via a scaling symmetry of the equation.

New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method

The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE), (2 + 1)-dimensional Davey-Stewartson system, and generalized Hirota-Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner. This method can also be applied to nonintegrable equations as well as integrable ones.

Differential invariants for Hirota–Ramani equation and Drinfel’d–Sokolov–Wilson system

In this paper, the differential invariants of Lie symmetry groups of Hirota–Ramani (HR) equation and Drinfel’d–Sokolov–Wilson (DSW) system are obtained and their syzygies and recurrence relations are classified. The algorithms are based on the method of equivariant moving frames.

The First Integral Method for the Generalized Drinfel’d–Sokolov–Wilson system and Bretherton equation

First integral method, which is called also FIM, in short, is usually applied to nonlinear partial differential equations. This method usually leads to an exact solution. This manuscript, the first integral method is applied to find exact Solitons solutions of the generalized forms of Drinfel’d–Sokolov–Wilson system, and Bretherton equation. FIM is based on the theory of commutative algebra.

First Integral Method to Study Nonlinear Evolution Equations

In this paper, we apply the first integral method to generalized ZK-BBM equation and Drinefel’d-Sokolov- Wilson system and one-dimensional modified EW-Burgers equation. The first integral method is a powerful solution method for obtaining exact solutions of some nonlinear evolution equations. This method was first proposed by Feng [8] in solving Burgers– KdV equation which is based on the ring theory of commutative algebra. This method can be applied to nonintegrable equations as well as to integrable ones. Key words First integral method; Generalized ZK-BBM equation ; Drinefel’d-Sokolov-Wilson system; One-dimensional modified EW-Burgers equation

Conservation laws for a complexly coupled KdV system, coupled Burgers’ system and Drinfeld–Sokolov–Wilson system via multiplier approach

The multiplier approach (variational derivative method) is used to derive the conservation laws for some nonlinear systems of partial differential equations. Firstly, the multipliers (characteristics) are computed and then conserved vectors are obtained for the each multiplier. Examples of the third-order complexly coupled KdV system, second-order coupled Burgers’ system and third-order Drinfeld–Sokolov–Wilson system are considered. For all three systems the local conservation laws are established by utilizing the multiplier approach.