Riemann-Hilbert approach to TD equation with nonzero boundary condition

Abstract

We extend the Riemann-Hilbert approach to the TD equation, which is a highly nonlinear differential integrable equation. Zero boundary condition at infinity for the TD equation is not suitable. Inverse scattering transform for this equation involves the singular Riemann-Hilbert problem, which means that the sectionally analytic functions have singularities on the boundary curve. Regularization procedures of the singular Riemann-Hilbert problem for two cases, the general case and the case for reflectionless potentials, are considered. Solitonic solutions to the TD equation are given.

Keywords

Riemann-Hilbert problem / singular / TD equation

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