Related papers: Nonlinear waves in the terrestrial quasi-parallel …
We study analytically and numerically a frequency downshifting due to power-type frequency-dependent decay of surface waves in the ocean covered by ice floes. The downshifting is obtained both within the linear model and within the…
We introduce a non-overlapping variant of the Schwarz waveform relaxation algorithm for semilinear wave propagation in one dimension. Using the theory of absorbing boundary conditions, we derive a new nonlinear algorithm. We show that the…
Sea ice attenuates waves propagating from the open ocean. Here we model the evolution of energetic unidirectional random waves in the marginal ice zone with a nonlinear Schr\"{o}dinger equation, with a frequency dependent dissipative term…
Recently, a nonlinear stability theory has been developed for wave trains in reaction-diffusion systems relying on pure $L^\infty$-estimates. In the absence of localization of perturbations, it exploits diffusive decay caused by smoothing…
We investigate dynamical aspects of the discrete nonlinear Schr\"{o}dinger equation (DNLS) in finite lattices. Starting from a periodic chain with nearest neighbor interactions, we insert randomly links connecting distant pairs of sites…
We study a defocusing quasilinear Schr\"odinger equation with nonzero conditions at infinity in dimension one. This quasilinear model corresponds to a weakly nonlocal approximation of the nonlocal Gross--Pitaevskii equation, and can also be…
An explanation is given for previous numerical results which suggest a certain bifurcation of `vector solitons' from scalar (single-component) solitary waves in coupled nonlinear Schroedinger (NLS) systems. The bifurcation in question is…
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…
Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
Existence and bifurcation results are derived for quasi periodic traveling waves of discrete nonlinear Schrodinger equations with nonlocal interactions and with polynomial type potentials. Variational tools are used. Several concrete…
In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions…
We study nonlinear waves in Newton's cradle, a classical mechanical system consisting of a chain of beads attached to linear pendula and interacting nonlinearly via Hertz's contact forces. We formally derive a spatially discrete modulation…
We extend the One-Way Navier Stokes (OWNS) approach to support nonlinear interactions between waves of different frequencies, which will enable nonlinear analysis of instability and transition. In OWNS, the linearized Navier-Stokes…
In this paper, we study the nonlinear modulational instability of two-dimensional hydroelastic Stokes waves in infinite depth. We first justify a focusing cubic nonlinear Schr\"odinger (NLS) approximation result for 2D deep hydroelastic…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless…
In \cite{one}, we have introduced the Born-Oppenheimer (BO) renormalization group approach to high energy hadronic collisions and derived the BO approximation for the light cone wave function of a fast moving projectile hadron. In this…
We study the evolution of a wave packet in a nonlinear Schr\"odinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue…
1. Introduction, 2. The (quasi-parallel) foreshock; Ion foreshock, Ion foreshock boundary region; Diffuse ions;Low-frequency upstream waves; Ion beam waves; The expected wave modes; Observations; Diffuse ion waves; Electron foreshock;…
Quantized nonlinear lattice models are considered for two different classes, boson and fermionic ones. The quantum discrete nonlinear Schroedinger model (DNLS) is our main objective, but its so called modified discrete nonlinear (MDNLS)…