N-th-Order Solutions for the Reverse Space-Time Nonlocal mKdV Equation: Riemann–Hilbert Approach

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 correspondi...

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Bibliographic Details
Published in:Symmetry (Basel) 2024-12, Vol.16 (12), p.1697
Main Authors: Lin, Bingwen, Zhang, Yongshuai
Format: Article
Language:English
Subjects:
Boundary conditions
double-periodic solution
higher-order poles
Inverse problems
reverse space-time nonlocal mKdV equation
Riemann–Hilbert approach
S matrix theory
Scattering coefficient
Spacetime
Symmetry
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Summary: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.
ISSN:2073-8994
DOI:10.3390/sym16121697