Kadomtsev-Petviashvili equation: one-constraint method and lump pattern
Jie-Yang Dong, Liming Ling, Xiaoen Zhang
TL;DR
This paper develops a method to construct high-dimensional solutions of the Kadomtsev-Petviashvili equation using lower-dimensional solutions and Darboux transformations, revealing connections between rogue waves and lump solutions.
Contribution
It introduces a one-constraint method for the KP equation that links rogue wave and lump solutions through asymptotic analysis.
Findings
Established a relationship between rogue waves and lump solutions.
Provided asymptotic analysis of lump patterns in the KP equation.
Demonstrated the use of lower-dimensional solutions to generate high-dimensional solutions.
Abstract
The Kadomtsev-Petviashvili reduction method is a crucial method to derive the solitonic solutions of (1+1) dimensional integrable system from high dimensional system. In this work, we explore to use the solutions of lower dimensional system to construct the solutions in the high dimensional one with the Darboux transformation. Especially, we utilize this method to disclose the relationship between the rogue wave and lump solutions. Under one-constraint method, the asymptotic analysis to the lump pattern of Kadomtsev-Petviashvili equation is given
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Fractional Differential Equations Solutions