相关论文: Existence of travelling waves in discrete sine-Gor…
We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term $\gamma$ and a linear dissipative…
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…
We prove the existence of periodic travelling wave solutions for general discrete nonlinear Klein-Gordon systems, considering both cases of hard and soft on-site potentials. In the case of hard on-site potentials we implement a fixed point…
For the nonlinear Klein-Gordon equation in R 1+d , we prove the existence of multi-solitary waves made of any number N of decoupled bound states. This extends the work of C{\^o}te and Mu{\~n}oz (Forum Math. Sigma 2 (2014)) which was…
We consider the problem of existence and stability of solitary traveling waves for the one dimensional discrete non linear Schroedinger equation (DNLS) with cubic nonlinearity, near the continuous limit.We construct a family of solutions…
We give arguments for the existence of {\it exact} travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a…
We study the spectral stability properties of periodic traveling waves in the sine-Gordon equation, including waves of both subluminal and superluminal propagation velocities as well as waves of both librational and rotational types. We…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…
We give a geometric proof of spectral stability of travelling kink wave solutions to the sine-Gordon equation. For a travelling kink wave solution of speed $c \neq \pm 1$, the wave is spectrally stable. The proof uses the Maslov index as a…
We study surface gravity waves for viscous fluid flows governed by Darcy's law. The free boundary is acted upon by an external pressure posited to be in traveling wave form with a periodic profile. It has been proven that for any given…
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…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
We consider a lattice equation modelling one-dimensional metamaterials formed by a discrete array of nonlinear resonators. We focus on periodic travelling waves due to the presence of a periodic force. The existence and uniqueness results…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and…
In the framework of hyperbolic conservation laws regularised by including diffusive and dispersive terms, we study monotone travelling waves for the generalised Rosenau-Korteweg de Vries equation. We establish existence as well as linear…
The existence of smooth periodic traveling solutions in the Dullin-Gottwald-Holm (DGH) equation and the monotonicity of the period function are clarified. By introducing two suitable parameters, we show the existence of periodic travelling…
We study Klein-Gordon chains with attractive nearest neighbour forces and convex on-site potential, and show that there exists a two-parameter family of periodic travelling waves (wave trains) with unimodal and even profile functions. Our…
In this paper, we determine spectral stability results of periodic waves for the critical Korteweg-de Vries and Gardner equations. For the first equation, we show that both positive and zero mean periodic traveling wave solutions possess a…