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matrix spectral problem

European Journal of Applied Mathematics (1)

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Inverse scattering transforms for non-local reverse-space matrix non-linear Schrödinger equations
Part of
- Infinite-dimensional Hamiltonian systems
- Equations of mathematical physics and other areas of application
WEN-XIU MA, YEHUI HUANG, FUDONG WANG
Journal:

European Journal of Applied Mathematics / Volume 33 / Issue 6 / December 2022

Published online by Cambridge University Press:

01 December 2021, pp. 1062-1082
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The aim of the paper is to explore non-local reverse-space matrix non-linear Schrödinger equations and their inverse scattering transforms. Riemann–Hilbert problems are formulated to analyse the inverse scattering problems, and the Sokhotski–Plemelj formula is used to determine Gelfand–Levitan–Marchenko-type integral equations for generalised matrix Jost solutions. Soliton solutions are constructed through the reflectionless transforms associated with poles of the Riemann–Hilbert problems.