Exact Solutions, Deformed Integrable NLS Equation and Riemann Problem

Abstract

The methodology of Riemann-Hilbert transform is adopted to obtain exact solution of the deformed NLS equation;
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deduced by Burtsev et al. It is observed that the required analytic structure is determined by the “constant” part of the otherwise space-time dependent spectral parameter λ(x, t). Lastly a direct substitution verifies the solution.