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We consider the cubic defocusing nonlinear Schr¨odinger equation in the two dimensional torus. Fix s > 1. Colliander, Keel, Staffilani, Tao and Takaoka proved in [CKS+10] the existence of solutions wi...
We consider the random Schrodinger equation as it arises in the paraxial regime for wave propagation in random media. In the white noise limit it becomes the Ito-Schrodinger stochastic partial differe...
We consider the long time behavior of solutions of the d-dimensional linear Boltzmann equation that arises in the weak coupling limit for the Schrodinger equation with a time-dependent random potentia...
The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schr?dinger equation in an iterative process. However, the method...
Using several kinds of Darboux transformations, we standardize the non- canonical symplectic structure of Ablowitz-Ladik model (A-L model) of the Nonlinear Schrdinger Equation (NLSE), then we emplo...
Let T be a homogeneous tree and L the Laplace operator on T. We consider the semilinear Schrodinger equation associated to L with a power-like nonlinearity F of degree d. We first obtain dispersive es...
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...
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...
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 ...
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...
We introduce a novel generalization of the discrete nonlinear Schrodinger equation. It supports solitons that describe how proteins fold. As an example we scrutinize the villin headpiece HP35,an arch...
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...
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...
The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to two-dimensional inhomogeneous nonlinear Schr¨odinger equation are considered. On the other hand, other methods ...
The unstable system of plasma equations where an electron beam is injected under a high-frequency electric field is reduced to the variable -coefficient unstable nonlinear Schr&ouml;dinger (vcUNLS) eq...

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