Related papers: Symmetric waves are traveling waves
We present a novel numerical method for simulating the generation and propagation of surface gravity waves by vertical seabed displacements. The cornerstone of our method is the computation of a time dependent conformal map which…
In this work we prove the equivalence between three different weak formulations of the steady periodic water wave problem where the vorticity is discontinuous. In particular, we prove that generalised versions of the standard Euler and…
In recent years two nonlinear dispersive partial differential equations have attracted a lot of attention due to their integrable structure. We prove that both equations arise in the modeling of the propagation of shallow water waves over a…
We consider the traveling structure of symmetric solutions to the Rosenau-Kawahara-RLW equation and the perturbed R-KdV-RLW equation. Both equations are higher order perturbations of the classical KdV equation. For the Rosenau-Kawahara-RLW…
The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function such as to give a dynamical account of collapse. The resulting…
This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a…
We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
We study travelling wave solutions, that is, solutions of the form $v(t, x) = e^{i\lambda t}u(g(t)x)$, to nonlinear Schr\"odinger and Klein-Gordon equations on Riemannian manifolds, both compact and non-compact ones, with emphasis on the…
In this work we consider a Fisher-Kolmogorov equation depending on two exponential functions of the spatial variables. We study this equation from the point of view of symmetry reductions in partial differential equations. Through…
We consider a system of NLS with cubic interactions arising in nonlinear optics without Galilean symmetry. The absence of Galilean symmetry can lead to many difficulties, such as global existence and blowup problems; see [Comm. Partial…
This paper presents a pioneering investigation into the existence of traveling wave solutions for the two-dimensional Euler equations with constant vorticity in a curved annular domain, where gravity acts radially inward. This configuration…
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behavior at infinity is established. Some generalizations to nonautonomous radial…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
We derive a non-linear supersymmetric sigma-model for the transport of light (classical waves) through a disordered medium. We compare this model with the well-established non-linear sigma-model for the transport of electrons (Schroedinger…
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…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
We show that wave breaking occurs for the modified Camassa-Holm (mCH) equation. Next we classify all traveling wave solutions of the modified Camassa-Holm equation in the weak sense via parametrization of their maxima, minima and wave…
We consider a system of partial differential equations, of interest to plasma physics, and provide all its Lie point symmetries, with their respective invariant solutions. We also discuss some of its conditional and partial symmetries. We…
Starting form the Zakharov/Craig-Sulem formulation of the water-waves equations, we prove that one can define a pressure term and hence obtain a solution of the classical Euler equations. It is proved that these results hold in rough…