Normalized solutions of nonlinear Schrödinger equations

Of Nonlinear Schrödinger Equations

The authors suggest a new powerful tool for solving group classification problems, that is applied to obtaining the complete group classification in the class of nonlinear Schrödinger equations of the form iψt +∆ψ + F (ψ,ψ ∗) = 0.

Numerical study of fractional nonlinear Schrödinger equations.

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the ...

Soliton Solutions for Quasilinear Schrödinger Equations

Numerical Continuation for Nonlinear SchrÖdinger Equations

We discuss numerical methods for studying numerical solutions of N-coupled nonlinear Schrödinger equations (NCNLS), N = 2, 3. First, we discretize the equations by centered difference approximations. The chemical potentials and the coupling coefficient are treated as continuation parameters. We show how the predictor–corrector continuation method can be exploited to trace solution curves and su...

Analysis for Nonlinear Schrödinger Equations with Potential

We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besi...