We address the Gross–Pitaevskii (GP) equation with a periodic linear potential and a periodic sign-varying nonlinearity coefficient. Contrary to the claims in the previous works of Abdullaev et al. [PRE 77, 016604 (2008)] and Smerzi & Trombettoni [PRA 68, 023613 (2003)], we show that the intersite cubic nonlinear terms in the discrete nonlinear Schrödinger (DNLS) equation appear beyond the appl...

In this study, the (3+1)-dimensional Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, which is a mathematical model of non-absorption and dispersion in non-linear medium, sheds light on sound beam phenomenon, has physically important place, examined. order to find exact solution an effective reliable method, (G^'/G,1/G)-expansion used among analytical methods. The purpose method obtain more than...

We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: partial differentialxG(Hx). We find that the stability of steady states depends on dv/dq , the derivative of the interface velocity on the wave vector q of the steady state. If the standard nonlinearity vanishes, coarsening is possible, in principle, only if G is an odd function of Hx. In this case...

In this paper we examine a spatially two–dimensional forced, damped Boussinesq equation with quadratic nonlinearity. This equation describes small, nonlinear oscillations of a circular, elastic membrane in the presence of viscosity. The eigenfunction expansion method is used for the purpose of constructing solutions for small initial data analytically. The constructive method enables us to perf...

Let us consider the following problem. Imagine a homogeneous nonlinear medium in which only one type of wave with dispersion law co(k) may propagate. Let the nonlinearity of the medium be quadratic while the equation co(k~ + k~) = co(k0 + co(k2) (1) defines a nonzero manifold F whose codimension in kl, k2 space is unity. Equation (1) means that dispersion law co(k) allows decay processes. The n...

This work deals with the following viscoelastic heat equations logarithmic nonlinearity u t − <mml:m...

Introduction High intensity focused ultrasound (HIFU) is considered a noninvasive and effective technique for tumor ablation. Frequency and acoustic power are the most effective parameters for temperature distribution and the extent of tissue damage. The aim of this study was to optimize the operating transducer parameters such as frequency and input power in order to acquire suitable temperatu...