A set of travelling wave solutions to a hyperbolic generalization of the convectionreaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of the compactly supported soloutions, shock fronts, soliton-like solutions and peakons PACS codes: 02.30.Jr; 47.50.Cd; 83.10.Gr

The existence of solutions with localized solitary wave structures is one the significant characteristics nonlinear integrable systems. Darboux transformation (DT) a well-known method for constructing multi-soliton solutions, using type wave, systems, but there are still no reports on extending DT techniques to construct such fractional models. This article takes coupled Schrödinger (CNLS) equa...

Wave group dynamics is studied in the framework of the extended Korteweg-de Vries equation. The nonlinear Schrodinger equation is derived for weakly nonlinear wave packets, and the condition for modulational instability is obtained. It is shown that wave packets are unstable only for a positive sign of the coe cient of the cubic nonlinear term in the extended Korteweg-de Vries equation, and for...

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...

The Darboux-dressing transformations are applied to the Lax pair associated with systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both ‘bright’ and ‘dark’ soliton solutions. The general formalism is set up and the relevant equations are explicitly solved. Several instances of multicomponent wave equations of applicative interest, such as vector...

We study instability of a vortex soliton eφω,m(r) to iut +∆u+ |u| u = 0, for x ∈ R, t > 0, where n = 2, m ∈ N and (r, θ) are polar coordinates in R. Grillakis [11] proved that every radially standing wave solutions are unstable if p > 1+4/n. However, we do not have any examples of unstable standing wave solutions in the subcritical case (p < 1 + n/4). Suppose φω,m is nonnegative. We investigate...

Exact solutions to a nonlinear Schrödinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an infinite lattice we find a localized soliton-like solution. The existence requirements and stability of these solutions are discussed, and we find that our solutions are linearly stable in most cases. We also show that ...

In this paper, a generalized F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the (2 + 1)dimensional breaking soliton equations to illustrate the validity and advantages of the proposed method. As a result, many new and more general non-travelling wave and coefficient function solutions are obtained includin...

Three–wave nonlinear resonant interaction (TWRI) is typically encountered in the description of any conservative nonlinear medium where the nonlinear dynamics can be considered as a perturbation of the linear wave solution, the lowest–order nonlinearity is quadratic in the field amplitudes, the three–wave resonance can be satisfied [1]. Indeed TWRI is the lowest–order nonlinear effect for a sys...

We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these wave patterns is carried out by means of our modification of the direct algebraic balance method. In the case when the analytical description fails, we propose...