We show the existence, size and some absorbing properties of global attractors of the nonlinear wave equations with nonlinear dissipations like ρ(x, ut) = a(x)|ut|rut.

ABSTRACT The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain soli...

We continue work by the second author and co-workers on solitary wave solutions of nonlinear beam equations and their stability and interaction properties. The equations are partial differential equations that are fourth-order in space and second-order in time. First, we highlight similarities between the intricate structure of solitary wave solutions for two different nonlinearities; a piecewi...

A device-level simulation is presented for studying wave propagation along metal–insulator–semiconductor interconnects. A set of nonlinear equations is first formulated by combining the motion equations of charged carriers and Maxwell’s equations. The set of nonlinear equations is then transformed into the frequency domain, which leads to sets of nonlinear equations for the fundamental mode and...

The modified simple equation method is employed to find the exact traveling wave solutions involving parameters for nonlinear evolution equations namely, a diffusive predator-prey system, the Bogoyavlenskii equation, the generalized Fisher equation and the Burgers-Huxley equation. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wa...

With the aid of symbolic computation, a new extended Jacobi elliptic function expansionmethod is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some 12 Jacobi elliptic functions, are very effective to uniformly construct more new exact periodic solutions in terms of Jacobi elliptic function s...

efficiency of numerical methods is an important problem in dynamic nonlinear analyses. it is possible to use of numerical methods such as beta-newmark in order to investigate the structural response behavior of the dynamic systems under random sea wave loads but because of necessity to analysis the offshore systems for extensive time to fatigue study it is important to use of simple stable meth...

We prove a conjecture by De Giorgi, which states that global weak solutions of nonlinear wave equations such as w + |w|p−2w = 0 can be obtained as limits of functions that minimize suitable functionals of the calculus of variations. These functionals, which are integrals in space-time of a convex Lagrangian, contain an exponential weight with a parameter ε, and the initial data of the wave equa...

Diffusion equations with degenerate nonlinear source terms arise in many different applications, e.g., in the theory of epidemics, in models of cortical spreading depression, and in models of evaporation and condensation in porous media. In this paper, we consider a generalization of these models to a system of n coupled diffusion equations with identical nonlinear source terms. We determine si...

The problems under consideration are related to wave propagation in nonlinear dispersive media, characterised by higher-order nonlinear and higher-order dispersive effects. Particularly two problems — wave propagation in dilatant granular materials and wave propagation in shape-memory alloys — are studied. Model equations are KdVlike evolution equations in both cases. The types of solutions are...