Work

Asymptotic Behavior Analysis of Solutions for the Coupled WKI Type Equation With the Schwartz Initial Data

Year: 2025

Type: article

Abstract: ABSTRACT For the Cauchy problem of the coupled WKI type equation associated with a matrix Lax pair with the Schwartz initial data, the long‐time asymptotics behavior of solutions is studied by using the nonlinear steepest descent method. First, based on the inverse scattering transformation, a matrix Riemann–Hilbert problem is constructed, and the potentials are exactly reconstructed by resorting to the asymptotic behavior of the eigenfunctions near and . Then, the multisoliton solutions of the coupled WKI type equation are obtained and the interaction dynamics of various soliton solutions are analyzed by selecting suitable parameters. Finally, the basic Riemann–Hilbert problem is transformed into a solvable model Riemann–Hilbert problem by a series of deformations, from which the long‐time asymptotics of the Cauchy problem of the coupled WKI type equation is obtained in the solitonless sector.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.11024

Authors: Wenhao Liu, Xiaowei Qin, Xianguo Geng

Institutions: China University of Mining and Technology, Zhengzhou University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze

Funder: National Natural Science Foundation of China

Awards: G3470053903, G3493690244, G4066400183