230 research outputs found
Exact Solutions for Domain Walls in Coupled Complex Ginzburg - Landau Equations
The complex Ginzburg Landau equation (CGLE) is a ubiquitous model for the
evolution of slowly varying wave packets in nonlinear dissipative media. A
front (shock) is a transient layer between a plane-wave state and a zero
background. We report exact solutions for domain walls, i.e., pairs of fronts
with opposite polarities, in a system of two coupled CGLEs, which describe
transient layers between semi-infinite domains occupied by each component in
the absence of the other one. For this purpose, a modified Hirota bilinear
operator, first proposed by Bekki and Nozaki, is employed. A novel
factorization procedure is applied to reduce the intermediate calculations
considerably. The ensuing system of equations for the amplitudes and
frequencies is solved by means of computer-assisted algebra. Exact solutions
for mutually-locked front pairs of opposite polarities, with one or several
free parameters, are thus generated. The signs of the cubic gain/loss, linear
amplification/attenuation, and velocity of the coupled-front complex can be
adjusted in a variety of configurations. Numerical simulations are performed to
study the stability properties of such fronts.Comment: Journal of the Physical Society of Japan, in pres
Application of Bernoulli Sub-ODE Method For Finding Travelling Wave Solutions of Schrodinger Equation Power Law Nonlinearity
In this paper, the exact travelling wave solution of the Schr¨odinger equation with power law nonlinearity is studied by the Sub-ODE method. It is shown that the method is one of the most effective approaches for finding exact solutions of nonlinear differential equations
Generalized and Improved (G'/G)-Expansion Method for Nonlinear Evolution Equations
A generalized and improved (G'/G)-expansion method is proposed for finding more general type
and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty
and advantage of the proposed method, we solve the KdV equation, the Zakharov-Kuznetsov-
Benjamin-Bona-Mahony �ZKBBM� equation and the strain wave equation in microstructured
solids. Abundant exact travelling wave solutions of these equations are obtained, which include
the soliton, the hyperbolic function, the trigonometric function, and the rational functions. Also
it is shown that the proposed method is efficient for solving nonlinear evolution equations in
mathematical physics and in engineering
- …