Abstract
With the help of the “dressing procedure” the singular Riemann problem corresponding to the Cauchy problem for the nonlinear Schrödinger equation with boundary conditions of finite density type is reduced to a regular Riemann problem. From the asymptotic analysis of the regular Riemann problem we get the principal term of the asymptotic solution of the Cauchy problem in the domain of superpolynomial decrease, which is described in terms of the scattering data corresponding to the initial condition.
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