E. V. Trifonov, “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”, TMF, 2017, Volume 192, Number 1,Pages <nobr>41

This article is cited in 3 papers

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

E. V. Trifonov^ab

^a Institute of Automation and Control Processes, Far Eastern Branch, RAS, Vladivostok, Russia
^b Far Eastern Federal University, Vladivostok, Russia

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.

Keywords: exact solution, wave equation, Bäcklund transformation.

Received: 21.07.2016
Revised: 16.11.2016

DOI: 10.4213/tmf9263