期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 402, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.physd.2019.132170
关键词
Nonlocal mKdV equation; Non-zero boundary conditions; Riemann surface; Inverse scattering transform; Matrix Riemann-Hilbert problem; Solitons
资金
- NSFC, China [11731014, 61621003, 11925108]
- CAS, China Interdisciplinary Innovation Team
In this paper, we present a systematical inverse scattering transform for both focusing and defocusing nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV) equations with non-zero boundary conditions (NZBCs) at infinity. The suitable uniformization variable is introduced to make the direct and inverse scattering problems be established on a new complex plane instead of the two-sheeted Riemann surface. The direct scattering problem establishes the analyticity, symmetries and asymptotic behaviors of Jost solutions and scattering matrix, and properties of discrete spectrum. The inverse scattering problem is solved by means of a corresponding matrix-valued Riemann-Hilbert problem. The reconstruction formula for the potential, trace formulae, and theta conditions are found. Finally, the dynamical behaviors of solitons and their interactions for four distinct cases of the reflectionless potentials for both focusing and defocusing nonlocal mKdV equations with NZBCs are analyzed in detail. (C) 2019 Elsevier B.V. All rights reserved.
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