In this paper, we study the properties of approximate solutions to a doubly nonlinear and degenerate diffusion equation, known in the literature as the diffusive wave approximation of the shallow water equations (DSW), using a numerical approach based on the Galerkin finite element method. This equation arises in shallow water flow models when special assumptions are used to simplify the shallo...

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this paper a set of approximate equations is derived which is applicable to very nonadiabatic, nondissipative, buoyant flows of a perfect gas. The flows are assumed to be generated by a heat source in which the heat is added slowly. The study is motivated by the occurrence of such flows in fires.There, the time scale associated with the fire growth and resultant fluid motion is usually long ...

In this paper, a variable coefficient generalized dispersive water-wave system which can model the propagation of the long weakly nonlinear and weakly dispersive surface waves of variable depth in shallow water is presented. With the aid of symbolic computation and using the generalized (G ′ G )-expansion method, the exact traveling wave solutions of this system are obtained. It is shown that t...

In the last two decades there has been considerable research on model water wave equations and the stability of their solitary waves. Among them, the Boussinesq type models such as [2], [3] and [4] describe small amplitude long waves in water of finite length. In this paper we will study the one-dimensional Benney-Luke equation. Our goal is twofold we aim to illustrate the usefulness of the abs...

In this work we present a further analytical development and a numerical implementation of the recently suggested theoretical model for highly nonlinear potential long-crested water waves, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in the conformal variables [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Numerical experim...

The equations describing planar magnetoacoustic waves of permanent form in a cold plasma are rewritten so as to highlight the presence of a naturally small parameter equal to the ratio of the electron and ion masses. If the magnetic field is not nearly perpendicular to the direction of wave propagation, this allows us to use a multiple-scale expansion to demonstrate the existence and nature of ...

A fully nonlinear modal analysis identifies a critical centerline wave number q(c) for river meandering that separates long-wavelength bends, which grow to cutoff, from short-wavelength bends, which decay. Exact, numerical, and approximate analytical results for q(c) rely on the Ikeda, Parker, and Sawai [J. Fluid Mech. 112, 363 (1981)] model, supplemented by dynamical equations that govern the ...

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrödinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term ...