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Abstract
Many equations possess soliton resonances phenomenon, this paper studies the soliton resonances of the nonisospectral modified Kadomtsev-Petviashvili (mKP) equation by asymptotic analysis.
Highlights
In the process of searching for explicit solutions, quite a few systematic methods have been developed, such as inverse scattering transformation [1], Darboux transformations [2], Hirota’s bilinear method [3,4,5], and so on
Many equations possess soliton resonances phenomenon, this paper studies the soliton resonances of the nonisospectral modified Kadomtsev-Petviashvili equation by asymptotic analysis
These structures provide a solution of the problem of “Mach reflection” in water waves, and this phenomenon is known as soliton resonance
Summary
In the process of searching for explicit solutions, quite a few systematic methods have been developed, such as inverse scattering transformation [1], Darboux transformations [2], Hirota’s bilinear method [3,4,5], and so on. As the interacting of the solution, soliton resonance has been studied in many papers. Miles obtained resonantly interacting solitary waves of KP equation [6], these solutions are coherent structures that describe the diffraction of a soliton at a corner, and suggest that, under certain conditions, a KP soliton can’t turn at a convex corner without separating or otherwise losing its identity. These structures provide a solution of the problem of “Mach reflection” in water waves, and this phenomenon is known as soliton resonance. The peak of the soliton is on the line i cons tan t
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