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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: Many-body Theory II

MP 11.2: Talk

Thursday, March 21, 2024, 09:50–10:10, HL 102

Special techniques in the auxiliary equation method for solving nonlinear differential equations — •Alina-Maria Păuna — Department of Physics, University of Craiova, 13 A.I. Cuza Street, 200585 Craiova, Romania

This report refers to a special approach that can be used in the method of auxiliary equations to solve complex nonlinear differential equations. More precisely, we will consider the coupling between a nonlinear differential equation whose solutions are sought and an auxiliary equation with already known solutions. The coupling between the two equations allows to find the most general form of the considered nonlinear equation that remains compatible, in terms of its solutions, with the given auxiliary equation.

The approach will be illustrated for the particular case when the nonlinear equation to be solved is a second-order reaction-diffusion equation with polynomial coefficients. Such equations describe important nonlinear phenomena that occur in hydrodynamics, optics, or plasma physics. The general approach we are proposing will be illustrated on several nonlinear equations, by generating their solutions when the elliptic Jacobi equation is considered as an auxiliary equation

Keywords: nonlinear partial differential equations; auxiliary equations