Related papers: On multichannel solutions of nonlinear Schr\"{o}di…
The coupled cubic nonlinear Schr\"odinger (CNLS) equations are used to study modulational instabilities of a pair of nonlinearly interacting two-dimensional waves in deep water. It has been shown that the full dynamics of these interacting…
The Nonlinear Schr\"odinger (NLS) equation is widely used in everywhere of natural science. Various nonlinear excitations of the NLS equation have been found by many methods. However, except for the soliton-soliton interactions, it is very…
The solution of nonlinear Schroedinger equation with saturation was found by means the quadratures method in terms of degeneracy theory. It was shown the existence conditions for soliton solutions.
The nonlinear Schr\"{o}dinger-Helmholtz (SH) equation in $N$ space dimensions with $2\sigma$ nonlinear power was proposed as a regularization of the classical nonlinear Schr\"{o}dinger (NLS) equation. It was shown that the SH equation has a…
We study the nonlinear stage of the modulation instability of a condensate in the framework of the focusing Nonlinear Schr\"{o}dinger Equation. We find a general N-solitonic solution of the focusing NLSE in the presence of a condensate by…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
A nonlinear Schr\"{o}dinger (NLS) equation with an effect of viscosity is derived from a Korteweg-de Vries (KdV) equation modified with viscosity using the method of multiple time-scales. It is well known that the plane-wave solution of the…
We consider a stochastic nonlinear Schr\"odinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing stochastic NLS in $H^1$ on compact manifolds and bounded domains. We construct a…
We discuss the behavior of solitary wave solutions of the nonlinear Schr{\"o}dinger equation (NLSE) as they interact with complex potentials, using a four parameter variational approximation based on a dissipation functional formulation of…
The nonlinear Schr{\"o}dinger (NLS) equation is a ubiquitous example of an envelope wave equation for conservative, dispersive systems. We revisit here the problem of self-similar focusing of waves in the case of the focusing NLS equation…
The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is…
The modulational stability of the nonlinear Schr{\"o}dinger (NLS) equation is examined in the cases with linear and quadratic external potential. This study is motivated by recent experimental studies in the context of matter waves in…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
We apply the spectral element method to the determination of scattering and bound states of the multichannel Schr\"odinger equation. In our approach the reaction coordinate is discretized on a grid of points whereas the internal coordinates…
We propose a class of numerical methods for the nonlinear Schr\"odinger (NLS) equation that conserves mass and energy, is of arbitrarily high-order accuracy in space and time, and requires only the solution of a scalar algebraic equation…
We investigate the presence of localized analytical solutions of the Schr\"odinger equation with logarithm nonlinearity. After including inhomogeneities in the linear and nonlinear coefficients, we use similarity transformation to convert…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…
We prove new local and global well-posedness results for the cubic one-dimensional nonlinear Schr\"odinger equation in modulation spaces. Local results are obtained via multilinear interpolation. Global results are proven using conserved…
By applying a simple symmetry reduction on a two-layer liquid model, a nonlocal counterpart of it is obtained. Then a general form of nonlocal nonlinear Schrodinger (NNLS) equation with shifted parity, charge-conjugate and delayed time…
The Whitham modulation equations for the defocusing nonlinear Schrodinger (NLS) equation in two, three and higher spatial dimensions are derived using a two-phase ansatz for the periodic traveling wave solutions and by period-averaging the…