Related papers: Bidirectional shallow-water wave turbulence
Physics of nonlinear waves on variable backgrounds and the relevant mathematical analysis continues to be the challenging aspect of the study. In this work, we consider a (3+1)-dimensional nonlinear model describing the dynamics of {water…
A Boussinesq system for a non-linear shallow water is considered. The nonlinear and topological effects are examined through an associated matrix spectral problem. It is shown an equivalence relationship between the bound states and…
The paper continues to study the long-standing problem of quasi 1-D (one dimensional) spectrum of sea surface wave turbulence. The study is based on Hasselmann's kinetic equation, which significantly simplifies for the quasi 1-D turbulence.…
Numerical simulations of the unidirectional random waves are performed within the Korteweg -de Vries equation to investigate the statistical properties of surface gravity waves in shallow water. Nonlinear evolution shows the relaxation of…
We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation.…
The purpose of this article is numerical verification of the theory of weak turbulence. We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial…
A generalized version of the $abcd$-Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conservation of suitable energy functionals in some cases and…
We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system,…
A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field $\boldsymbol{B_0} = B_0 \hat{\boldsymbol{e}}_\|$. This regime is relevant…
Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable systems was discovered. In the diffusionless limit, this is equivalent to a certain "Bethe-Boltzmann" kinetic equation, which has the form of an…
We study a self-similar solution of the kinetic equation describing weak wave turbulence in Bose-Einstein condensates. This solution presumably corresponds to an asymptotic behavior of a spectrum evolving from a broad class of initial data,…
One-parameter families of exact two-component solitary-wave solutions for interacting high-frequency (HF) and low-frequency (LF) waves are found in the framework of Zakharov-type models, which couple the nonlinear Schr\"odinger equation…
The Boussinesq-Klein-Gordon (BKG) equation has emerged in the studies of nonlinear bulk strain waves in layered solid waveguides. The developed bi-directional weakly-nonlinear solution leads to two copies of the Ostrovsky equation, for the…
The linear stability of a rotating, stratified, inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. An energy argument is used to show that unstable perturbations must have…
We report on direct numerical simulation of quasi-one-dimensional bidirectional capillary-wave turbulence. Although nontrivial three-wave and four-wave resonant interactions are absent in this peculiar geometry, we show that an energy…
In this work, we investigate non-classical wavetrain formations, and particularly dispersive shock waves (DSWs), or undular bores, in systems exhibiting non-convex dispersion. Our prototypical model, which arises in shallow water wave…
In this paper we study the existence of periodic travelling waves for the 2D $abcd$ Boussinesq type system related with the three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. We show that small solutions that…
Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…
It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves, which have been not reported for other mainstream models of shallow water waves. In this letter, the closed-form solutions of peaked solitary waves of…
We study the universal non-stationary evolution of wave turbulence (WT) in Bose-Einstein condensates (BECs). Their temporal evolution can exhibit different kinds of self-similar behavior corresponding to a large-time asymptotic of the…