scholarly journals A Riemann-Hilbert Approach to the Multicomponent Kaup-Newell Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jian-bing Zhang ◽  
Ze-xuan Zhang
Keyword(s):  
Inverse Scattering ◽  
Soliton Solutions ◽  
Scattering Problems ◽  
Jump Matrix ◽  
Inverse Scattering Problems ◽  
Reflectionless Potential

A Riemann-Hilbert approach is developed to the multicomponent Kaup-Newell equation. The formula is presented of N -soliton solutions through an identity jump matrix related to the inverse scattering problems with reflectionless potential.

scholarly journals Inverse Scattering and Soliton Solutions of Nonlocal Complex Reverse-Spacetime Modified Korteweg-de Vries Hierarchies

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 512
Author(s):  
Liming Ling ◽  
Wen-Xiu Ma
Keyword(s):  
Inverse Scattering ◽  
Soliton Solutions ◽  
Identity Matrix ◽  
Nonlocal Symmetry ◽  
Scattering Problems ◽  
Spectral Problems ◽  
Symmetry Reductions ◽  
Jump Matrix ◽  
De Vries ◽  
Scattering Transforms

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.

A diagonalized improved subspace-based optimization method for solving 2-D inverse scattering problems

2017 ◽  
Vol 59 (8) ◽  
pp. 2089-2095 ◽  
Author(s):  
Yulang Liu ◽  
Zhiqin Zhao ◽  
Xiaozhang Zhu ◽  
Wei Yang ◽  
Zaiping Nie ◽  
...  
Keyword(s):  
Inverse Scattering ◽  
Optimization Method ◽  
Scattering Problems ◽  
Inverse Scattering Problems

Dual regularization in non-linear inverse scattering problems

2016 ◽  
Vol 24 (7) ◽  
pp. 1215-1239 ◽  
Author(s):  
Konstantin P. Gaikovich ◽  
Petr K. Gaikovich ◽  
Yelena S. Maksimovitch ◽  
Alexander I. Smirnov ◽  
Mikhail I. Sumin
Keyword(s):  
Inverse Scattering ◽  
Scattering Problems ◽  
Inverse Scattering Problems ◽  
Dual Regularization ◽  
Non Linear
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