Shallow water inertio-gravity Poincaré waves in a rotating frame satisfy the Klein–Gordon equation, originally derived for relativistic, spinless quantum particles. Here, we compare these two superficially unrelated phenomena, suggesting reason them sharing same equation. We discuss their energy conservation laws and equivalency between non-relativistic limit of yielding Schrödinger near-inerti...

This paper describes the effects of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluids in an asymmetric channel. The two dimensional equation of couple stress fluid are simplified by making the assumptions of long wave length and low Reynolds number. The exact solutions of reduced momentum equation and magnetic force function have been computed in wave...

The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the surface wave solutions. The appropriate solutions satisfy the required boundary conditions at the stress-free surface to obtain the frequency equation of Rayleigh wave. The numerical values of the non-dimensional speed of Rayleigh wave speed are computed for different values of frequency...

We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the oneand two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)],...

We present a two-dimensional vertical (2DV) flow and morphological numerical model describing the behaviour of offshore sand waves. The model contains the 2DV shallow water equations, with a free water surface and a general bed load formula. The water movement is coupled to the sediment transport equation by a seabed evolution equation. Using this model, we investigate the evolution of sand wav...

Interaction of two long-crested shallow water waves is analysed in the framework of the two-soliton solution of the Kadomtsev-Petviashvili equation. The wave system is decomposed into the incoming waves and the interaction soliton that represents the particularly high wave hump in the crossing area of the waves. Shown is that extreme surface elevations up to four times exceeding the amplitude o...

We propose an algorithm for an asymptotic model of shallow-water wave dynamics in a periodic domain. The algorithm is based on the Hamiltonian structure of the equation and corresponds to a completely integrable particle lattice. In particular, “periodic particles” are introduced in the algorithm for waves travelling through the domain. Each periodic particle in this method travels along a char...

Reciprocal transformations [1-3] are a useful tool in the study of integrable partial differential equations. Recently, there has been much interest in the equation of Fokas-Fuchssteiner-CamassaHolm (FFCH), originally derived by Fokas and Fuchssteiner [4] in the context of bi-Hamiltonian theory, and subsequently rederived as an equation for shallow water waves by Camassa and Holm [5]. The FFCH ...

The existence of solitary-wave solutions to the three-dimensional water-wave problem with strong surface-tension effects is predicted by the KP-I model equation. The term solitary wave describes any solution which has a pulse-like profile in its direction of propagation, and the KP-I equation admits explicit solutions for three different types of solitary wave. A line solitary wave is spatially...