Riemann–Hilbert Problems and Soliton Solutions of Type ( λ ∗, − λ ∗ ) Reduced Nonlocal Integrable mKdV Hierarchies

Wen-Xiu Ma
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Wen-Xiu Ma: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Mathematics, 2022, vol. 10, issue 6, 1-21

Abstract: Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the matrix Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems. One reduction is local, which replaces the spectral parameter λ with its complex conjugate λ ∗ , and the other one is nonlocal, which replaces the spectral parameter λ with its negative complex conjugate − λ ∗ . Riemann–Hilbert problems and thus inverse scattering transforms are formulated from the reduced matrix spectral problems. In view of the specific distribution of eigenvalues and adjoint eigenvalues, soliton solutions are constructed from the reflectionless Riemann–Hilbert problems.

Keywords: matrix spectral problem; zero curvature equation; group reduction; Riemann–Hilbert problem; soliton solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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