Electron. J. Differential Equations, Vol. 2023 (2023), No. 82, pp. 1-16.

Variety of solutions and dynamical behavior for YTSF equations

Wei Chen

We construct non-homogeneous polynomial lump wave solutions of the Yu-Toda-Sasa-Fukuyama (YTSF) equation, based on a bilinear approach, enriching the formal diversity of lump waves. By studying the interaction between the lump solutions of the YTSF equation and the solitary wave solutions, we find a new aggregation effect and elastic collision effect. We obtain exact solutions, such as the solution of separated variables and periodic nonlinear wave solutions, by applying the Lie symmetry group method and the bilinear method.

Submitted April 27, 2023. Published December 10, 2023.
Math Subject Classifications: 35B35, 35B40.
Key Words: YTSF equation; symmetry reduction; two-lump wave; aggregation; interaction wave.
DOI: 10.58997/ejde.2023.82

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Wei Chen
School of Mathematical Sciences
University of Science and Technology of China
Hefei, Anhui, 230026, China
email: chenwei7@mail.ustc.edu.cn

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