相关论文: Multi-solitons and related solutions for the water…
Families of solutions to the field equations of the covariant BRST invariant effective action of the membrane theory are constructed. The equations are discussed in a double dimensional reduction, they lead to a nonlinear equation for a one…
A coupled Volterra system is proposed. The model can be considered as one of the integrable discrete form of the coupled integrable KdV system which is a significant physical model. Many types of cnoidal waves, positons, negatons (solitons)…
Some effects of surface tension on fully-nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are…
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…
We consider the equivariant wave maps equation $\mathbb{R}^{1+2} \to \mathbb{S}^2$, in all equivariance classes $k \in \mathbb{N}$. We prove that every finite energy solution resolves, continuously in time, into a superposition of…
We establish long time soliton asymptotics for the nonlinear system of Maxwell equations coupled to a charged particle. The coupled system has a six dimensional manifold of soliton solutions. We show that in the long time approximation, any…
We consider finite energy corotationnal wave maps with target manifold $\m S^2$. We prove that for a sequence of times, they decompose as a sum of decoupled harmonic maps in the light cone, and a smooth wave map (in the blow case) or a…
We consider the quadratic semilinear wave equation in six dimensions. This energy critical problem admits a ground state solution, which is the unique (up to scaling) positive stationary solution. We prove that any spherically symmetric…
This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved that the energy decays to zero exponentially in time,…
In this paper, we investigate the formation of singularity for general two dimensional and radially symmetric solutions for rotating shallow water system from different aspects. First, the formation of singularity is proved via the study…
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\"odinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to…
Many equations that arise in a physical context can be posed in the form of a Hamiltonian system, meaning that there is a symplectic structure on an appropriate phase space, and a Hamiltonian functional with respect to which time evolution…
We consider the asymptotic behavior of the soltion to the wave equation with time-dependent damping and analytic nonlinearity. Our main goal is to prove the convergence of a global solution to an equilibrium as time goes to infinity by…
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…
A system of coupled scalar fields is introduced which possesses a spectrum of massive single-soliton solutions. Some of these solutions are unstable and decay into lower mass stable solitons. Some properties of the solutions are obtained…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
We construct 2-solitons of any speed of the focusing energy-critical nonlinear wave equation in dimension 5. The existence result also holds for the case of K-solitons, for any K >2, assuming that the speeds are collinear. The main…
We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons [see Phys.…
Main goal of this note is to give a result for nonexistence of global solutions and determine the critical exponent as well to a semi-linear structurally damped wave equation.
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…