We relate the scattering theory of the focusing AKNS system with equally sized nonvanishing boundary conditions to that of the matrix Schrodinger equation. This (shifted) Miura transformation converts the focusing matrix nonlinear Schrodinger (NLS) equation into a new nonlocal integrable equation. We apply the matrix triplet method of solving the Marchenko integral equations by separation of variables to derive the multisoliton solutions of this nonlocal equation, thus proposing a method to solve the reflectionless matrix NLS equation.
A Matrix Schrodinger Approach to Focusing Nonlinear Schrodinger Equations with Nonvanishing Boundary Conditions
Demontis, F
;van der Mee, C
2022-01-01
Abstract
We relate the scattering theory of the focusing AKNS system with equally sized nonvanishing boundary conditions to that of the matrix Schrodinger equation. This (shifted) Miura transformation converts the focusing matrix nonlinear Schrodinger (NLS) equation into a new nonlocal integrable equation. We apply the matrix triplet method of solving the Marchenko integral equations by separation of variables to derive the multisoliton solutions of this nonlocal equation, thus proposing a method to solve the reflectionless matrix NLS equation.
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