Multi-wave solutions for a non-isospectral KDV-type equation with variable coefficients

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.

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-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...

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

Backlund Transformation and N-soliton-like Solutions to the Combined KdV-Burgers Equation with Variable Coefficients

Abstract: In this paper, through a new transformation, the combined KdvBurgers equation with variable coefficients(vcKdvB) is reduced to a new simplified equation.Based on the homogeneous balance principle(HBP),we studied the Backlund transformation(BT) and several exact soliton-like solutions to this vcKdvB equation. Including single kink-like solitary wave solutions, double-soliton-like solut...