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Classifying algebraic invariants and algebraically invariant solutions

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  • Demina, Maria V.

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.

Suggested Citation

  • Demina, Maria V., 2020. "Classifying algebraic invariants and algebraically invariant solutions," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306159
    DOI: 10.1016/j.chaos.2020.110219
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