Families of exact solutions for linear and nonlinear wave equations with a variable speed of sound and their use in solving initial boundary value problems

Abstract

We propose a procedure for multiplying solutions of linear and nonlinear one-dimensional wave equations, where the speed of sound can be an arbitrary function of one variable. We obtain exact solutions. We show that the functional series comprising these solutions can be used to solve initial boundary value problems. For this, we introduce a special scalar product.