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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...
Delta function singularity in the Reduction of Radial Schrodinger Equation
Laplace operator radial equation boundary condition singular potentials
2010/12/8
We obtain the extra delta-like singularity while reduction of the Laplace operator in spherical coordinates, elimination of which restricts the radial wave functions at the origin. This restriction ha...
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...
On the effect of random inhomogeneities in Kerr-media modelled by non-linear Schrodinger equation
Kerr-media modelled non-linear Schrodinger equation
2010/4/6
We consider propagation of optical pulses under the interplay of dispersion and Kerr non-linearity in optical fibres with impurities distributed at random uniformly on the fibre. By using a model base...