Energy supercritical nonlinear Schrödinger equations: Quasiperiodic solutions

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.

A minimal energy tracking method for non-radially symmetric solutions of coupled nonlinear Schrödinger equations

We aim at developing methods to track minimal energy solutions of time-independent mcomponent coupled discrete nonlinear Schrödinger (DNLS) equations. We first propose a method to find energy minimizers of the 1-component DNLS equation and use it as the initial point of the m-component DNLS equations in a continuation scheme. We then show that the change of local optimality occurs only at the b...

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...

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 ...