Nonlinear Mathematical Models for Physical Phenomena

摘要

The paper focuses on methods which allow to directly finding traveling wave solutions for a specific class of partial differential equations. The key idea is the reduction of the initial equation to an ordinary differential equation by passing to the wave variable. An improvement to the classical approach, consisting in a supplementary reduction by attaching a flux type equation, is proposed. How this improved approach is working is illustrated on few nonlinear models describing physical phenomena.