相关论文: Traveling waves of a generalized Rotation-Camassa-…
It is well known that the Coriolis force due to Earth's rotation can induce wind veer in the mean flow velocity of an atmospheric boundary layer (ABL), but much less is known about its effects on turbulent coherent structures. In this work,…
We emphasize that construction of travelling wave solutions for partial differential equations is a problem of considerable interest and thus introduce a simple algebraic method to generate such solutions for equations in the Burgers…
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…
Differential rotation plays a key role in stellar evolution by triggering hydrodynamical instabilities and large-scale motions that induce transport of chemicals and angular momentum and by modifying the propagation and the frequency…
Rotation is a crucial characteristic of fluid flow in the atmosphere and oceans, which is present in nearly all meteorological and geophysical models. The global existence of solutions to the 3D Navier-Stokes equations with large rotation…
In this paper, we investigate the spectral instability of periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Kadomtsev-Petviashvili equation. By…
For the generalized $p$-power Korteweg-de Vries equation, all non-periodic travelling wave solutions with non-zero boundary conditions are explicitly classified for all integer powers $p\geq 1$. These solutions are shown to consist of:…
We describe the physical hypotheses underlying the derivation of an approximate model of water waves. For unidirectional surface shallow water waves moving over an irrotational flow as well as over a non-zero vorticity flow, we derive the…
This work studies the rotation-generalized Benjamin-Ono equation which is derived from the theory of weakly nonlinear long surface and internal waves in deep water under the presence of rotation. It is shown that the solitary-wave solutions…
We prove the existence of a global bifurcation branch of $2\pi$-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly…
In this paper, we study traveling wave solutions and peakon weak solutions of the modified Camassa-Holm (mCH) equation with dispersive term $2ku_x$ for $k\in\mathbb{R}$. We study traveling wave solutions through a Hamiltonian system…
Context. Differential rotation has a strong influence on stellar internal dynamics and evolution, notably by triggering hydrodynamical instabilities, by interacting with the magnetic field, and more generally by inducing transport of…
In this paper, we explore the orbital stability of smooth solitary wave solutions to the modified Camassa-Holm equation with cubic nonlinearity. These solutions, which exist on a nonzero constant background $k$, are unique up to translation…
In this paper we review the physical relevance of a Korteweg-de Vries (KdV) equation with higher-order dispersion terms which is used in the applied sciences and engineering. We also present exact traveling wave solutions to this…
We study an equation lying `mid-way' between the periodic Hunter-Saxton and Camassa-Holm equations, and which describes evolution of rotators in liquid crystals with external magnetic field and self-interaction. We prove that it is an Euler…
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…
The Hartle-Hawking wave function is known to be the Fourier dual of the Chern-Simons or Kodama state reduced to mini-superspace, using an integration contour covering the whole real line. But since the Chern-Simons state is a general…
In this paper, we investigate the global conservative solutions to the generalized Camassa-Holm equation with dual-power nonlinearities. By introducing a new set of variables, we transform the original equation into an equivalent…
By a bifurcation argument we prove that the capillary-gravity Whitham equation features asymmetrical periodic travelling wave solution of arbitrarily small amplitude. Such waves exist only in the weak surface tension regime…
We evaluate the impact of the rotation on the stochastic excitation of acoustic (p) modes in solar-like pulsators. First, we derive the forced wave equation taking rotation into account and we compute the source terms, which inject energy…