N-th-Order Solutions for the Reverse Space-Time Nonlocal mKdV Equation: Riemann–Hilbert Approach
Year: 2024
Type: article
Abstract: This paper explores the reverse space-time mKdV equation through the application of the Riemann–Hilbert problem. Under the zero boundary condition, we derive the Jost solutions, examine their the analytic and symmetry properties alongside those of the scattering matrix, and formulate the corresponding Riemann–Hilbert problem. By assuming that the scattering coefficient has multiple simple zero points and one higher-order zero point, we obtain explicit solutions to the Riemann–Hilbert problem in a reflection-less situation and display two types of formulae for the N-th order solutions of the reverse space-time nonlocal mKdV equation, which correspond to multiple simple poles and one higher-order pole, respectively. As applications, we display two kinds of double-periodic solutions explicitly and graphically. Additionally, we display the conversation laws for the reverse space-time nonlocal mKdV equation.
Source: Symmetry
DOI: 10.3390/sym16121697
Authors: Bingwen Lin, Yongshuai Zhang
Institutions: Lishui University, Shaoxing University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
OpenAlex ID: W4405726469