Abstract We consider the dispersion managed power-law nonlinear Schrödinger (DM NLS) equations with a small parameter ɛ &gt; 0 and averaged equation, which are used in optical fiber communications. prove that solutions of DM NLS converge to solution equation <m...

We prove dynamical dichotomy into scattering and blow-up (in a weak sense) for all radial solutions of the Zakharov system in energy space four spatial dimensions that have less than ground state, which is written using Aubin-Talenti function. The characterized by critical mass wave component state. result similar to Kenig Merle energy-critical nonlinear Schr\"odinger equation (NLS). Unlike NLS...

We prove global well-posedness for low regularity data for the L 2 − critical defocusing nonlinear Schrödinger equation (NLS) in 2d. More precisely we show that a global solution exists for initial data in the Sobolev space H s (R 2) and any s > 2 5. This improves the previous result of Fang and Grillakis where global well-posedness was established for any s ≥ 1 2. We use the I-method to take a...

The dynamics of a one-dimensional slowly modulated, nearly monochromatic localized wave train in deep water is described by a one-dimensional soliton solution of a twodimensional nonlinear Schrödinger (NLS) equation. In this paper, the instability of such a wave train with respect to transverse perturbations is examined numerically in the context of the NLS equation, using Hill’s method. A vari...

We present a study of the existence, stability, and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocusing nonlinear Schrödinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features...

We consider a general class of discrete nonlinear Schrödinger equations (DNLS) on the lattice hZ with mesh size h > 0. In the continuum limit when h → 0, we prove that the limiting dynamics are given by a nonlinear Schrödinger equation (NLS) on R with the fractional Laplacian (− ) as dispersive symbol. In particular, we obtain that fractional powers 1 2 < α < 1 arise from long-range lattice int...

In this paper we study the performance of time-splitting spectral approximations for general nonlinear Schrödinger equations (NLS) in the semiclassical regimes, where the Planck constant ε is small. The time-splitting spectral approximation under study is explicit, unconditionally stable and conserves the position density in L1. Moreover it is time-transverse invariant and timereversible when t...