Related papers: Trapped solitary-wave interaction for Euler equati…
Linear limit continuation was recently developed as a systematic and effective method for constructing numerically exact solitary waves from their respective linear limits. In this work, we apply the technique to two typical anisotropic…
We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional…
To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the…
We study the dynamics of one electron wave packet in a chain with a non-adiabatic electron-phonon interaction. The electron-phonon coupling is taken into account in the time-dependent Schr\"odinger equation by a delayed cubic nonlinearity.…
This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain (a nonintegrable system) and compares the simulation results with the theoretical results in fluid (an integrable system). Three…
Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the…
The nonlinear dynamics of waves at the sea surface is believed to be ruled by the Weak Turbulence framework. In order to investigate the nonlinear coupling among gravity surface waves, we developed an experiment in the Coriolis facility…
It is shown that the interaction of a plasma with thermal radiation leads to the stabilization of both periodic and solitary nonlinear plasma waves. The stabilized periodic nonlinear plasma waves were indeed observed in the experiment…
We show that a Bose-Einstein condensate and a portion of its surrounding thermal cloud can exhibit mutual self-trapping, supported by the attractive particle interactions, and not by the external confinement. This type of dynamics is…
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped…
Quantum entanglement occurs not just in discrete systems such as spins, but also in the spatial wave functions of systems with more than one degree of freedom. It is easy to introduce students to entangled wave functions at an early stage,…
This paper proves existence and stability results of solitary-wave solutions to coupled nonlinear Schr\"{o}dinger equations with power-type nonlinearities arising in several models of modern physics. The existence of solitary waves is…
In this paper we review the results of the author on the theory of scalar and vector wave scattering by small bodies of an arbitrary shape with the emphasis on practical applicability of the formulas obtained and on the mathematical rigor…
In this paper, persistence of solitary wave solutions of the regularized long wave equation with small perturbations are investigated by the geometric singular perturbation theory. Two different kinds of the perturbations are considered in…
Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in…
Systems consisting of cold atoms trapped near photonic crystal waveguides have recently emerged as an exciting platform for quantum atom-light interfaces. Such a system enables realization of tunable long-range interactions between internal…
Linear arrays of trapped and laser cooled atomic ions are a versatile platform for studying emergent phenomena in strongly-interacting many-body systems. Effective spins are encoded in long-lived electronic levels of each ion and made to…
We consider the wave equation in a bounded domain (eventually convex). Two kinds of inequality are described when occurs trapped ray. Applications to control theory are given. First, we link such kind of estimate with the damped wave…
We demonstrate experimentally the existence of three-wave resonant interaction solitary triplets in quadratic media. Stable velocity-locked bright-dark-bright spatial solitary triplets, determined by the balance between the energy exchange…
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…