Classifying algebraic invariants and algebraically invariant solutions

Maria V. Demina

Chaos, Solitons & Fractals, 2020, vol. 140, issue C

Abstract: A concept of algebraic invariants and algebraically invariant solutions for autonomous ordinary differential equations and systems of autonomous ordinary differential equations is considered. A variety of known exact solutions of autonomous ordinary differential equations and a great number of traveling wave solutions of famous partial differential equations are in fact algebraically invariant solutions. A method, which can be used to find all irreducible algebraic invariants, is introduced. As an example, all irreducible algebraic invariants for the traveling wave reductions of the dispersive Kuramoto–Sivashinsky equation and the modified Kuramoto–Sivashinsky equation are classified. Novel solutions of the modified Kuramoto–Sivashinsky equation are obtained.

Keywords: Algebraic invariants; Algebraically invariant solutions; Algebraic traveling waves; Dispersive Kuramoto–Sivashinsky equation; Modified Kuramoto–Sivashinsky equation (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306159

DOI: 10.1016/j.chaos.2020.110219

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