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Zhao, Zhonglong; He, Lingchao

\(M\)-lump and hybrid solutions of a generalized \((2+1)\)-dimensional Hirota-Satsuma-Ito equation. (English) Zbl 1450.35116

Appl. Math. Lett. 111, Article ID 106612, 8 p. (2021).
Summary: In this paper, the \(N\)-soliton solutions of a generalized \((2+1)\)-dimensional Hirota-Satsuma-Ito equation are obtained by means of the bilinear method. By applying the long wave limit to the \(N\)-solitons, the \(M\)-lump waves are constructed. The propagation orbits, velocities and the collisions among the lumps of the \(M\)-lump waves are analyzed. Three kinds of high-order hybrid solutions are presented, which contain the hybrid solution between lumps and solitons, a 1-lump and 1-breather, and a \(m\)-breather and \(n\)-soliton. The results are helpful to explain some nonlinear phenomena of the generalized shallow water wave model.

Cited in 16 Documents

MSC:

35C08 Soliton solutions
35C07 Traveling wave solutions
35G25 Initial value problems for nonlinear higher-order PDEs
35Q35 PDEs in connection with fluid mechanics

Keywords:

\(N\)-soliton solutions; \(M\)-lump solutions; generalized shallow water wave model
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References:

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