Interactions of certain localized waves for an extended \((3+1)\)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics. (English) Zbl 07858889
Summary: Currently, there is much interest in the study on the localized waves and their interactions in fluid mechanics. An extended \((3+1)\)-dimensional Kadomtsev-Petviashvili equation is considered here. By means of the Hirota method, we obtain the \(N\)-soliton solutions, with \(N\) as a positive integer. The higher-order breather solutions are obtained from the \(N\)-soliton solutions through the complex conjugated transformations. Making use of the long-wave limit method, we determine the higher-order lump solutions via the \(N\)-soliton solutions. Besides, some hybrid solutions are presented. Three kinds of the localized waves, namely, the solitons, breathers and lumps, along with their interactions, are investigated via the above solutions. Amplitudes, shapes and velocities of those localized waves remain invariant after the interactions, which indicate that the interactions are elastic. Fluid-mechanically meaningful, all our results rely on the coefficients in that equation.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q51 | Soliton equations |
| 35C05 | Solutions to PDEs in closed form |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 68W30 | Symbolic computation and algebraic computation |
Keywords:
soliton; breather; lump; interaction; extended \((3+1)\)-dimensional Kadomtsev-Petviashvili equationReferences:
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