Laplace type invariants for variable coefficient mKdV equations

The extended Riccati equation mapping method for variable-coefficient diffusion-reaction and mKdV equations

Explicit exact solutions for variable coefficient Broer-Kaup equations

Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient Broer-Kaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient Broer...

New Exact Solutions of a Variable-coefficient Mkdv Equation

In this paper, negatons, positons and complexiton solutions of higher order for a non-isospectral MKdV equation, the MKdV equation with loss and nonuniformity terms are obtained through the bilinear Bäcklund transformation. AMS Subject Classification: 35Q53

VARIABLE COEFFICIENT THIRD ORDER KdV TYPE OF EQUATIONS

We show that the integrable subclassess of the equations q,t = f(x, t) q,3 + H(x, t, q, q,1) are the same as the integrable subclassess of the equations q,t = q,3 + F (q, q,1).

Laplace-Type Semi-Invariants for a System of Two Linear Hyperbolic Equations by Complex Methods

In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations PDEs in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied semiinvariants for systems of two linear hyperbolic PDEs in two independent variables. Separately, by splitting ...