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Cauchy problem of nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2
Applied mathematics Cauchy problem nonlinear Schrodinger equation local well-posedness scaling limit
2011/10/15
In this paper, we consider in R^n the Cauchy problem for nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2. It is well known that this problem is ill posed. However, We...
On asymptotic stability of moving ground states of the nonlinear Schrodinger equation
asymptotic stability nonlinear Schrodinger equation Analysis of PDEs
2011/9/20
Abstract: We extend to the case of moving solitons, the result on asymptotic stability of ground states of the NLS with a short range linear potential obtained by the author in a previous paper. Now w...
Nonlinear-damping continuation of the nonlinear Schrodinger equation - a numerical study
Nonlinear-damping continuation nonlinear Schrodinger equation Analysis of PDEs
2011/9/13
Abstract: We study the nonlinear-damping continuation of singular solutions of the critical and supercritical NLS. Our simulations suggest that for generic initial conditions that lead to collapse in ...
Nonautonomous "rogons" in the inhomogeneous nonlinear Schrodinger equation with variable coefficients
Inhomogeneous NLS equation with variable coefficients Similarity transformation
2010/12/16
The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr¨odinger equation with variable coefficients in terms of rational-like functions by using the similarity transforma...