Related papers: Two-Parameter Method for Describing the Nonlinear …
The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this…
This paper presents a computational framework for modeling wave propagation in geometrically linear elastic materials characterized by algebraically nonlinear constitutive relations. We derive a specific form of the nonlinear wave equation…
We prove that line solitons of the two-dimensional hyperbolic nonlinear Schr\"odinger equation are unstable with respect to transverse perturbations of arbitrarily small periods, {\em i.e.}, short waves. The analysis is based on the…
The analysis of nonlinear spectroscopy, widely used to study the dynamics and structures of condensed-phase matter, typically employs a perturbative approach noticing the weak interaction between the laser and the matter of interest.…
We analytically study nonlinear quasi-monochromatic plasma waves in a two-dimensional electron system set between the two metal electrodes (gates). We derive a nonlinear Schrodinger equation for a slow-varying envelope to describe the…
We study the propagation of femtosecond light pulses inside an optical fiber medium exhibiting higher-order dispersion and cubic-quintic nonlinearities. Pulse evolution in such system is governed by a higher-order nonlinear Schr%…
We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly…
We are interested in the stability of a class of totally geodesic wave maps, as recently studied by Abbrescia and Chen, and later by Duan and Ma. The relevant equations of motion are a system of coupled semilinear wave and Klein-Gordon…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…
A computational fluid model is developed to study waves and instabilities. A new technique involving initial perturbations in configuration space have been implemented to excite the plasma waves; i.e. the perturbations acting similar to a…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' $q$-nonextensive statistics.…
We obtain solutions to the coupled Schr\"odinger-Poisson equations. The solutions describe the evolution of cold dark matter density perturbations in an otherwise homogeneous expanding Friedmann universe. We discuss the relationships…
Nonlinear deformations of a two-dimensional gas bubble are investigated in the framework of a Hamiltonian formulation involving surface variables alone. The Dirichlet--Neumann operator is introduced to accomplish this dimensional reduction…
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…
This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein--Gordon equations and the Maxwell--Lorentz system. The interest here is in…
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem…
We consider coupled nonlinear Schrodinger equations (CNLSE) which govern the propagation of nonlinear waves in bimodal optical fibers. The nonlinear transform of a dual-frequency signal is used to generate an ultra-short-pulse train. To…
We identify the nonlinear evolution equation in impact-parameter space for the "Supercritical Pomeron" in Reggeon Field Theory as a 2-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and…
Group velocity and group velocity dispersion for a wave packet in vectorial discrete Klein-Gordon models are obtained by an expansion, based on perturbation theory, of the linear system giving the dispersion relation and the normal modes.…