相关论文: Coupled nonlinear Schrodinger systems with potenti…

In this paper, the trial function method is employed to find the exact solutions for high-order nonlinear Schr\"odinger equations with time-dependent coefficients. This system describes the propagation of ultrashort light pulses in…

We present basic results, known and new, on nontrivial solutions of periodic stationary nonlinear Schr\"odinger equations. We also sketch an application to nonlinear optics and discuss some open problems.

Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the…

We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…

The soliton dynamics in the semiclassical limit for a weakly coupled nonlinear focusing Schr\"odinger systems in presence of a nonconstant potential is studied by taking as initial data some rescaled ground state solutions of an associate…

We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…

We consider stationary and propagating solutions for a Bose-Einstein condensate in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate…

Existence and bifurcation results are derived for quasi periodic traveling waves of discrete nonlinear Schrodinger equations with nonlocal interactions and with polynomial type potentials. Variational tools are used. Several concrete…

Understanding, predicting, and controlling physical processes often relies on the analysis of the dynamics of partial differential equations (PDEs). In this context, the present study offers an in-depth investigation into the nonlinear…

This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein--Gordon equations and the Maxwell--Lorentz system. The interest here is in…

We consider combining of multiple laser beams into a single near diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. The beams with the total power above critical are combined in the near field and then propagated in…

We consider the stationary solutions for a class of Schrodinger equations with a N-well potential and a nonlinear perturbation. By means of semiclassical techniques we prove that the dominant term of the ground state solutions is described…

The initial value problem for some defocusing coupled nonlinear Schrodinger equations is investigated. Global well-posedness and scattering are established.

We study the Cauchy problem for Schrodinger equations with repulsive quadratic potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a…

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…

We are interested in finding a family of solutions to a singularly perturbed biharmonic equation which has a concentration behavior. The proof is based on variational methods and it is used a weak version of the Ambrosetti-Rabinowitz…

It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…

Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…

We investigate dark-bright vector solitary wave solutions to the coupled non-linear Schr\"odinger equations which describe an inhomogeneous two-species Bose-Einstein condensate. While these structures are well known in non-linear fiber…

Using similarity transformations we construct explicit solutions of the nonlinear Schrodinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their…