Bernd Fritzsche, Bernd Kirstein, Inna Ya. Roitberg, Alexander L. Sakhnovich, “Pseudo-Exponential-Type Solutions of Wave Equations Depending on Several Variables”, SIGMA, 2015, Volume 11,010, 13 pp.

This article is cited in 2 papers

Pseudo-Exponential-Type Solutions of Wave Equations Depending on Several Variables

Bernd Fritzsche^a, Bernd Kirstein^a, Inna Ya. Roitberg^a, Alexander L. Sakhnovich^b

^a Fakultät für Mathematik und Informatik, Universität Leipzig, Augustusplatz 10, D-04009 Leipzig, Germany
^b Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria

Abstract: Using matrix identities, we construct explicit pseudo-exponential-type solutions of linear Dirac, Loewner and Schrödinger equations depending on two variables and of nonlinear wave equations depending on three variables.

Keywords: Bäcklund–Darboux transformation; matrix identity; $S$-node; $S$-multinode; explicit solution; non-stationary Dirac equation; non-stationary Schrödinger equation; Loewner system; pseudo-exponential-type potential; integrable nonlinear equations.

MSC: 35C08; 35Q41; 15A24

Received: September 4, 2014; in final form January 23, 2015; Published online January 29, 2015

Language: English

DOI: 10.3842/SIGMA.2015.010