A new class of solutions for the multi-component extended Harry Dym equation

2017/05/04 by Michal Marvan, Marvan, Michal, M. V. Pavlov +2
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.1705.01792

arxiv created 2017/05/04 · openalex publication_date 2017/05/04 · arxiv updated 2017/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a point transformation between two integrable systems, the multi-component Harry Dym equation and the multi-component extended Harry Dym equation, that does not preserve the class of multi-phase solutions. As a consequence we obtain a new type of wave-like solutions, generalising the~multi-phase solutions of the multi-component extended Harry Dym equation. Our construction is easily transferable to other integrable systems with analogous properties.

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