Related papers: Two dimensional solitary waves in shear flows
The two-dimensional free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth. We investigate how flows with small-amplitude Stokes waves on the free surface bifurcate from a horizontal parallel…
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…
We consider the CH-KP-I equation. For this equation we prove the existence of steady solutions, which are solitary in one horizontal direction and periodic in the other. We show that such waves bifurcate from the line solitary wave…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
We analyze the spectral and dynamical stability of solitary wave solutions to the Lugiato-Lefever equation (LLE) on $\mathbb{R}$. Our interest lies in solutions that arise through bifurcations from the phase-shifted bright soliton of the…
Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions 2+1 and 3+1. The solutions are in the form of infinite series involving cylindirical and spherical wave functions and they are…
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…
The existence of a solution to the two dimensional incompressible Euler equations in singular domains was established in [G\'erard-Varet and Lacave, The 2D Euler equation on singular domains, submitted]. The present work is about the…
We give a rigorous proof of existence for solitary waves of a peridynamics model in one space dimension recently investigated by Silling (J. Mech. Phys. Solids 96:121--132, 2016). We adapt the variational framework developed by Friesecke…
A basic example of shear flow was introduced by DiPerna and Majda to study the weak limit of oscillatory solutions of the Euler equations of incompressible ideal fluids. In particular, they proved by means of this example that weak limit of…
In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility…
We consider the spectra of the 2-dim gravity waves of finite depth linearized at a uniform monotonic shear flow $U(x_2)$, $x_2 \in (-h, 0)$, where the wave numbers $k$ of the horizontal variable $x_1$ is treated as a parameter. Our main…
This paper is concerned with decay and symmetry properties of solitary wave solutions to a nonlocal shallow water wave model. It is shown that all supercritical solitary wave solutions are symmetric and monotone on either side of the crest.…
We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of…
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…
We prove the existence of pure capillary solitary waves for the 2D finite-depth Euler equations with nonzero constant vorticity. In the irrotational case, nonexistence of solitary waves was established by Ifrim--Pineau--Tataru--Taylor, so…
In this paper we study a class of nonlinear Schr\"odinger equations which admit families of small solitary wave solutions. We consider solutions which are small in the energy space $H^1$, and decompose them into solitary wave and dispersive…
We interpret as shear viscosity the anisotropic pressure that emerges in inhomogeneous spherically symmetric spacetimes described by the Lemaitre-Tolman-Bondi (LTB) metric in a comoving frame. By assuming that local isotropic pressure and…
The solitary waves of massive (1+1)-dimensional nonlinear S^N-sigma models are unveiled. It is shown that the solitary waves in these systems are in one-to-one correspondence with the separatrix trajectories in the repulsive N-dimensional…
We prove that symmetric, doubly periodic, capillary-gravity water waves in finite depth bifurcating from non-uniform non-stagnant shear flows are necessarily two-dimensional to leading order. This is in stark contrast to the case of uniform…