Related papers: Delta shock wave and interactions in a simple mode…
The existence of local, classical solutions is proved, for a system of two coupled equations that describe, in the framework of the wave turbulence theory, the fluctuations around an equilibrium, of a system of nonlinear waves satisfying…
In two and three dimensions, the standard treatment of the scattering problem for a multi-delta-function potential, $v(\mathbf{r})=\sum_{n=1}^N\mathfrak{z}_n\delta(\mathbf{r}-\mathbf{a}_n)$, leads to divergent terms. Regularization of these…
This paper studies the stability and large-time behavior of the three-dimensional (3-D) Boltzmann equation near shock profiles. We prove the nonlinear stability of the composite wave consisting of two shock profiles under general…
A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic…
We consider the $L^2$-supercritical nonlinear Schr\"{o}dinger equation with a repulsive Dirac delta potential in one dimensional space. In a previous work, we clarified the global dynamics of even solutions with the same action as the…
Impulsive gravitational waves are (weak) solutions to the Einstein vacuum equations such that the Riemann curvature tensor admits a delta singularity along a null hypersurface. The interaction of impulsive gravitational waves is then…
We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify…
We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of…
We study a self-interacting scalar field theory in the presence of a \delta-function background potential. The role of surface interactions in obtaining a renormalizable theory is stressed and demonstrated by a two-loop calculation. The…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
The recently found shock wave solution in the scalar field model with the field potential $V(\phi)=|\phi|$ is generalized to the case $V(\phi)=|\phi|-{1/2}\lambda\phi^2$. We find two kinds of the shock waves, which are analogous of…
In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave and a long-wave in fluid dynamics, plasma physics and nonlinear optics, is considered. Using the…
We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a…
The Cauchy problem is considered for the perturbed strictly hyperbolic 2x2 system of quasilinear equations. The unperturbed problem has a persistent solution with two discontinuity lines (shock waves). Both an asymptotics of shock waves…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
We use an S-wave toy model for the two-nucleon system to show that the implicit renormalization of a contact theory matches the explicit renormalization through a flow equation which integrates out the high momentum components. By fitting…
Recent work has given a systematic way for studying the kinetics of classical weakly interacting waves beyond leading order, having analogies with renormalization in quantum field theory. An important context is weak wave turbulence,…
Pair soliton interactions play a significant role in the dynamics of soliton turbulence. The interaction of solitons with different polarities is particularly crucial in the context of abnormally large wave formation, often referred to as…
The interest in the Camassa-Holm equation inspired the search for various generalizations of this equation with interesting properties and applications. In this letter we deal with such a two-component integrable system of coupled…
We study experimentally the interaction between two solitary waves that approach one to another in a linear chain of spheres interacting via the Hertz potential. When these counter propagating waves collide, they cross each other and a…