Variable coefficient KdV equation with time-dependent variable coefficient topographic forcing term and atmospheric blocking

New Exact Solutions of a Variable-Coefficient KdV Equation

In this paper, we apply the Miura transformation to construct the connection between a variablecoefficient KdV (vcKdV) equation and a variable-coefficient modified KdV (vcmKdV) equation under certain constraint. Solving the vcmKdV equation by use of the auxiliary equation method and using the Miura transformation, we find a rich variety of new exact solutions for the vcKdV equation, which inclu...

Variable Coefficient KdV Equations and Waves in Elastic Tubes

We present a simplified one-dimensional model for pulse wave propagation through fluid-filled tubes with elastic walls, which takes into account the elasticity of the wall as well as the tapering effect. The spatial dynamics in this model is governed by a variable coefficient KdV equation with conditions given at the inflow site. We discuss an existence theory for the associated evolution equat...

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).

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

Domain Decomposition Algorithm for the Parabolic Equation with Variable Coefficient

In this paper, we design a domain decomposition algorithm for the two-dimensional parabolic equation with variable coefficient by using a larger spacing at interface points and the implicit scheme at the interior points, hence get an algorithm with the relaxed stability bounds. Then we prove the stability and analyze the accuracy of the algorithm by using the idea of maximum principle. Some res...