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We consider the one dimensional focusing (cubic) Nonlinear Schrodinger equation (NLS) in the semiclassical limit with exponentially decaying complex-valued initial data, whose phase is multiplied by a real parameter. We prove smooth dependence of the asymptotic solution on the parameter. Numerical results supporting our estimates of important quantities are presented.
A perturbation of a class of scalar Riemann-Hilbert problems (RHPs) with the jump contour as a finite union of oriented simple arcs in the complex plane and the jump function with a $zlog z$ type singularity on the jump contour is considered. The jum
The long-time asymptotic behavior of solutions to the focusing nonlinear Schrodinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the case of initial conditions that allow for the presence of discre
We consider the long-time properties of the an obstruction in the Riemann-Hilbert approach to one dimensional focusing Nonlinear Schrodinger equation in the semiclassical limit for a one parameter family of initial conditions. For certain values of t
The $n$-fold Darboux transformation $T_{n}$ of the focusing real mo-di-fied Kor-te-weg-de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the $n$-soliton solutions of the mKdV equation are als
We consider the nonlinear Schrodinger equation, with mass-critical nonlinearity, focusing or defocusing. For any given angle, we establish the existence of infinitely many functions on which the scattering operator acts as a rotation of this angle. U