Interaction structures of multi localized waves within the Kadomtsev-Petviashvili I equation

This paper investigates a (2+1)-dimensional Kadomtsev-Petviashvili I (KP I) equation, which describes the long waves in water with weak surface tension. The KP I equation can be reduced to a (1 + 1)-dimensional system consisting of a generalized multi component nonlinear Schrodinger (NLS) equation and a modified Korteweg-de Vries (mKdV) equation by using constraints the potential function of the KP I equation to its squared eigenfunction. So, any solution of the (1+1)-dimensional integrable system gives rise to a localized solution of the KP I equation. Then, according to the Lax pairs of the above (1 + 1)-dimensional system, the generalized (m, N - m)-fold Darboux transformation is adopted to explore various solutions. These solutions include single structure solutions, such as lump-chains, (N- 1)-th degenerate lump-chains and Nth-order lump, and especially interaction solutions of arbitrary structures formed on the basis of single structure solutions. As a consequence, the corresponding single structure and mixed interaction solutions for the KP I equation can be obtained by solving the (1 + 1)-dimensional system with generalized DT. Moreover, all these structure solutions are discussed analytically and shown graphically. Finally, we also sum up various mathematical features of mixed localized wave solutions. The results obtained in this paper may be helpful to understand the interaction phenomena of localized nonlinear waves in KP I equation.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the (2+1)-dimensional Kadomtsev-Petviashvili I (KP I) equation, which can be reduced to a (1+1)-dimensional system consisting of a generalized nonlinear Schrodinger (NLS) equation and a modified Korteweg-de Vries (mKdV) equation using constraints. The generalized (m, N - m)-fold Darboux transformation is used to explore various solutions, including single structure solutions and interaction solutions of arbitrary structures formed based on single structure solutions. The obtained structure solutions are discussed analytically and shown graphically, providing insight into the interaction phenomena of localized nonlinear waves in the KP I equation.