Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 010, 13 pages      arXiv:1305.2178      https://doi.org/10.3842/SIGMA.2015.010

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

Bernd Fritzsche a, Bernd Kirstein a, Inna Ya. Roitberg a and 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

Received September 04, 2014, in final form January 23, 2015; Published online January 29, 2015

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.

Key words: 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.

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