The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics

The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols This article presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices We also discuss the physics of wind-blown sand and dune formation on Venus and Titan

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The physics of wind-blown sand and dust

The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This paper presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars. Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices. We also discuss the physics of wind-blown sand and dune formation on Venus and Titan.

/pdf/the-physics-of-wind-blown-sand-and-dust-4ggy9vm6xy.pdf

Based on computerized symbolic computation and modified extended tanh-function method for constructing a new exact travelling wave solutions of nonlinear evolution equations (NEEs) is presented and implemented in a computer algebraic system. Applying this method, with the aid of Maple, we consider some (NEEs) with mathematical physics interests. As a results, we can successfully recover the previously known solitary wave solutions that had been found by the tanh-function method and other more sophisticated methods.

New exact travelling wave solutions using modified extended tanh-function method

We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the new Hamiltonian amplitude equation introduced by Wadati et al. When the modulus nt approaches to 1 and 0, then the hyperbolic function solutions (including the solitary wave solutions) and trigonometric function solutions are also given respectively. As the parameter s goes to zero, the new Hamiltonian amplitude equation becomes the well-known nonlinear Schrodinger equation (NLS), and at least there are 37 kinds of solutions of NLS can be derived from the solutions of the new Hamiltonian amplitude equation. (c) 2004 Elsevier Ltd. All rights reserved.

Tian-De Miao

Papers

The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations

Computer simulation of aeolian sand ripples and dunes

Surface waves in aeolian bedforms