相关论文: A tale of two Nekrasov's integral equations

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly coupled to an extra linear dissipative equation. The model describes, e.g., a two-layer liquid film…

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential…

The Degasperis-Procesi equation possesses well-known peaked solitary waves that are called peakons. Their stability has been established by Lin and Liu in [5]. In this paper, we localize the proof (in some suitable sense detailed in Section…

Consider a viscous fluid of finite depth below the air. In the absence of the surface tension effect at the air-fluid interface, the long time behavior of a free surface with small amplitude has been an intriguing question since the work of…

In this paper, we investigate the instability of one-dimensionally stable periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Zakharov-Kuznetsov…

We investigate theoretically and numerically the dynamics of long-living oscillating coherent structures - bi-solitons - in the exact and approximate models for waves on the free surface of deep water. We generate numerically the…

We study the large-time behavior of the 1D barotropic Navier-Stokes flow perturbed from Riemann data generating a composition of two shock waves with small amplitudes. We prove that the perturbed Navier-Stokes flow converges, uniformly in…

This review describes the discovery of gravitational waves. We recount the journey of predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental…

Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is an…

We show that the peaked periodic traveling wave of the reduced Ostrovsky equations with quadratic and cubic nonlinearity is spectrally unstable in the space of square integrable periodic functions with zero mean and the same period. The…

In this paper, we overview the recent progresses on the lifespan estimates of classical solutions of the initial value problems for nonlinear wave equations in one space dimension. There are mainly two directions of the developments on the…

The propagation of surface water waves over rough topographical bottoms is investigated by the multiple scattering theory. It is shown that the waves can be localized spatially through the process of multiple scattering and wave…

We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth, and prove a rigorous reduction of these equations to Birkhoff normal form up to degree four. This proves a conjecture of…

Free internal waves in polytropic atmospheres are studied (polytropic atmosphere is such one that the temperature of gas linearly depends on altitude). We suppose gas to be ideal and incompressible. Also, we regard the atmosphere of…

We present a rigorous mathematical analysis of the modeling of inviscid water waves. The free-surface is described as a parametrized curve. We introduce a numerically stable algorithm which accounts for its evolution with time. The method…

In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…

In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…

We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…

In this paper, we investigate the existence and spectral stability of periodic traveling wave solutions for the regularized Camassa-Holm equation. To establish the existence of periodic waves, we employ tools from bifurcation theory to…

In 1895, Korteweg and de Vries (KdV), derived their celebrated equation describing the motion of waves of long wavelength in shallow water. In doing so they made a number of quite reasonable assumptions, incompressibility of the water and…