Generalized solutions and Euler–Darboux transformations

I. V. Verevkin

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

Abstract: We introduce Euler–Darboux transformation for non-homogeneous differential equations with the right-hand side being a generalized function. As an example, we construct the fundamental solutions for Klein–Gordon–Fock and Schrödinger equations with variable coefficients describing a particle in external scalar field.

Keywords: Euler–Darboux transformation, Klein–Gordon–Fock equation, Schrödinger equation, fundamental solution.

UDC: 517.95

MSC: 35A08, 35D99, 35Q40

Received: 06.03.2014

 English version: Ufa Mathematical Journal, 2014, 6:4, 60–67

Bibliographic databases:

•