Introduction. We are going to present here some brief survey of the results of Theory of Solitons (see [1–3]) from the viewpoint of periodic theory including some new results in the theory of 2-dimensional periodic Schrodinger Operators. A remarkable connection of some very special but highly nontrivial nonlinear (especially one-dimensional) systems with spectral properties of one-dimensional l...

Abstract:In this paper, we utilize the Exp-function method with symbolic computational system Maple to constructing generalized solitary solutions of auxiliary equation. With the aid of auxiliary equation and its generalized solitary solutions, new exact solutions with three arbitrary functions of two nonlinear evolution equations in physics, namely, higher-order nonlinear Schrodinger equation ...

Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma. Keywords—Amplitude Modulation, Electron Pla...

From the discrete nonlinear Schrodinger equation describing transport on a dimer we derive and solve a closed nonlinear equation for the site-occupation probability difference. Our results, which are directly relevant to specific experiments such as neutron scattering in physically realizable dimers, exhibit a transition from "free" to "self-trapped" behavior and illustrate features expected in...

We analytically calculate and discuss the radio-frequency spectrum of the socalled Akhmediev breathers, a class of nonlinear solutions of the nonlinear Schrodinger equation that governs the propagation in a single mode optical fiber. We propose a practical application of ABs to the field of ultra-wideband pulse generation.

I’ll present some recent work with F. Planchon on bilinear virial identities for the nonlinear Schrodinger equation, which are extensions of the Morawetz interaction inequalities firstly obtained by Colliander, Keel, Staffilani, Takaoka and Tao. We recover and extend known bilinear improvements to Strichartz inequalities and provide applications to various nonlinear problems, most notably on do...