Journal
SYMMETRY-BASEL
Volume 13, Issue 3, Pages -Publisher
MDPI
DOI: 10.3390/sym13030512
Keywords
matrix spectral problem; soliton hierarchy; nonlocal PT symmetry; Riemann-Hilbert problem; Inverse scattering; soliton solution
Categories
Funding
- National Natural Science Foundation of China [11975145, 11972291, 11771151]
- Natural Science Foundation for Colleges and Universities in Jiangsu Province [17 KJB 110020]
- Guangzhou Science and Technology Program [201904010362]
- Fundamental Research Funds for the Central Universities [D2192580]
- Guagdong Natural Science Foundation [2017A030313008]
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This paper investigates the soliton solutions of nonlocal complex reverse-spacetime mKdV hierarchies through nonlocal symmetry reductions of matrix spectral problems. By formulating the corresponding inverse scattering problems and constructing solutions to specific Riemann-Hilbert problems, N-soliton solutions to the hierarchies are obtained.
This paper aims to explore nonlocal complex reverse-spacetime modified Korteweg-de Vries (mKdV) hierarchies via nonlocal symmetry reductions of matrix spectral problems and to construct their soliton solutions by the inverse scattering transforms. The corresponding inverse scattering problems are formulated by building the associated Riemann-Hilbert problems. A formulation of solutions to specific Riemann-Hilbert problems, with the jump matrix being the identity matrix, is established, where eigenvalues could equal adjoint eigenvalues, and thus N-soliton solutions to the nonlocal complex reverse-spacetime mKdV hierarchies are obtained from the reflectionless transforms.
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