This article shows how to use perturbation methods to get new examples of evolutionary partial differential equations with gradient-like structure. In particular, we investigate the case of the wave equation with a variable damping satisfying the geometric control condition only, and the case of the wave equation with a damping of indefinite sign.

In this paper we give sufficient condition for the Buckley-Feuring solution to exist by the variation iteration method are used for find the exact fuzzy solution of the fuzzy wave-like equation in one and two dimensions with variable coefficients and fuzzy parameters. Some examples are given to show the reliability and the efficiency of the sufficient condition..

in this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (srlw) equation and the (3+1)-dimensional shallow water wave equations. solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions the physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. note t...

The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of wave-kinetic equations, the so called Wigner–Moyal equations. These equations are coupled to a background radiation fluid, whose dynamics is determined by an...

In this work, we consider variable order difusion and wave equations. The derivative is describedin the Caputo sence of variable order. We use the Genocchi polynomials as basic functions andobtain operational matrices via these polynomials. These matrices and collocation method help usto convert variable order diusion and wave equations to an algebraic system. Some examples aregiven to show the...

We use He’s polynomials which are calculated form homotopy perturbation method HPM for solving heat and wave-like equations. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that suggested technique solves nonlinear problems without u...

It has been shown that velocity of propagation of wave front cannot coincide with observable velocity of quantum particles. It is additional argument leads to conclusion that phase wave of de Broglie cannot be associated with single “elementary” particle like electron. Therefore quantum interference under linear superposition cannot describe energy distribution in extended quantum particles. Es...

An approach of Green’s function is adopted to solve the inhomogeneous linear differential equations representing wave equations in piezo-composite materials. In particular, transference of horizontally polarised shear (SH) waves is considered in bedded structure comprising of porous-piezo electric layer lying over a heterogeneous half-space. Propagation of SH-waves is considered to be influence...

Travelling-wave solutions of the Degasperis–Procesi equation (DPE) are investigated. The solutions are characterized by two parameters. Hump-like, loop-like and coshoidal periodicwave solutions are found; hump-like, loop-like and peakon solitary-wave solutions are obtained as well. Hone and Wang showed a connection between the DPE and the Vakhnenko equation (VE). Comparing the solutions of the ...

We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: ho...