Exact self-similar and two-phase solutions of systems of semilinear parabolic equations
K.A. Volosov, V. G. Danilov, and A. M. Loginov (Moscow)
TL;DR
This paper presents exact self-similar and two-phase solutions for systems of semilinear parabolic equations, utilizing Painleve test and Hirota's method to construct solutions of Newell-Whitehead type.
Contribution
It introduces novel exact solutions for semilinear parabolic systems using Painleve and Hirota techniques, expanding the analytical solution set for these equations.
Findings
Exact single-wave solutions derived
Two-wave solutions constructed
Methods applicable to similar systems
Abstract
Exact single-wave and two-wave solutions of systems of equations of Newell-Whitehead type are presented. The Painleve test and calculations in the spirit of Hirota are used to construct these solutions.
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Taxonomy
TopicsNonlinear Waves and Solitons · Quantum chaos and dynamical systems · Fractional Differential Equations Solutions