Localized nonlinear waves in a semiconductor with charged dislocations

Nonlinear localized waves in a periodic medium.

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.

Localized waves in nonlinear oscillator chains.

This paper reviews results about the existence of spatially localized waves in nonlinear chains of coupled oscillators, and provides new results for the Fermi-Pasta-Ulam (FPU) lattice. Localized solutions include solitary waves of permanent form and traveling breathers which appear time periodic in a system of reference moving at constant velocity. For FPU lattices we analyze the case when the ...

On Nonlinear Water Waves in a Channel

Interaction of charged particles with localized electrostatic waves in a magnetized plasma.

Charged particle interaction with localized wave packets in a magnetic field is formulated using the canonical perturbation theory and the Lie transform theory. An electrostatic wave packet characterized by a wide range of group and phase velocities as well as spatial extent along and across the magnetic field is considered. The averaged changes in the momentum along the magnetic field, the ang...

Localized Nonlinear Waves in Nonlinear Schrödinger Equation with Nonlinearities Modulated in Space and Time

In this paper, the generalized sub-equation method is extended to investigate localized nonlinear waves of the one-dimensional nonlinear Schrödinger equation (NLSE) with potentials and nonlinearities depending on time and on spatial coordinates. With the help of symbolic computation, three families of analytical solutions of this NLS-type equation are presented. Based on these solutions, period...