Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

Order reduction and μ-conservation law for the non-isospectral KdV type equation a with variable-coefficients

The goal of this paper is to calculate of order reduction of the KdV typeequation and the non-isospectral KdV type equation using the μ-symmetrymethod. Moreover we obtain μ-conservation law of the non-isospectral KdVtype equation using the variational problem method.

Exact Solutions for a Generalized KdV-MKdV Equation with Variable Coefficients

By using solutions of an ordinary differential equation, an auxiliary equationmethod is described to seek exact solutions of variablecoefficient KdV-MKdV equation. As a result, more new exact nontravelling solutions, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, and combined Jacobi elliptic function solutions, for...

The modified KdV equation with variable coefficients: Exact uni/bi-variable travelling wave-like solutions

In this paper, the modified Korteweg-de Vries (mKdV) equation with variable coefficients (vc-mKdV equation) is investigated via two kinds of approaches and symbolic computation. On the one hand, we firstly reduce the vc-mKdV equation to a second-order nonlinear nonhomogeneous ODE using travelling wave-like similarity transformation. And then we obtain its many types of exact fractional solution...

Exact Solutions for a Generalized KdV Equation with Time-Dependent Coefficients and K(m,n) Equation

In this paper, a generalized KdV equation with time-dependent coefficients will be studied. The K(m,n) equation with generalized evolution will also be examined. The Riccati equation mapping method will be used to obtain some new exact solutions for both equations. These solutions include solitary wave solutions and periodic wave solutions. The results presented in this paper improve the previo...