20 research outputs found
Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method
AbstractNew exact travelling wave solutions for the double sinh-Gordon equation and its generalized form are formally derived by using the tanh method and the variable separated ODE method. The Painlevé property v = eu is employed to support the tanh method in deriving exact solutions. The work emphasizes the power of the methods in providing distinct solutions of different physical structures
New Travelling Wave Solutions for Sine-Gordon Equation
We propose a method to deal with the general sine-Gordon equation. Several new exact travelling wave solutions with the form of
JacobiAmplitude function are derived for the general sine-Gordon equation by using some reasonable transformation. Compared with previous solutions, our solutions are more general than some of the previous
Dynamics of multi-kinks in the presence of wells and barriers
Sine-Gordon kinks are a much studied integrable system that possesses
multi-soliton solutions. Recent studies on sine-Gordon kinks with
space-dependent square-well-type potentials have revealed interesting dynamics
of a single kink interacting with wells and barriers. In this paper, we study a
class of smooth space-dependent potentials and discuss the dynamics of one kink
in the presence of different wells. We also present values for the critical
velocity for different types of barriers. Furthermore, we study two kinks
interacting with various wells and describe interesting trajectories such as
double-trapping, kink knock-out and double-escape.Comment: 17 pages, 7 figure
Rogue waves and other solutions of single and coupled Ablowitz–Ladik and nonlinear Schrödinger equations
We provide a simple technique for finding the correspondence between the solutions of Ablowitz–Ladik and nonlinear Schrodinger equations. Even though they belong to different classes, in that one is continuous and one is discrete, there are matching solutions. This fact allows us to discern common features and obtain solutions of
the continuous equation from solutions of the discrete equation. We consider several examples. We provide tables, with selected solutions, which allow us to easily match the pairs of solutions. We show that our technique can be extended to the case of coupled Ablowitz–Ladik and nonlinear Schrodinger (i.e. Manakov) equations. We provide some new solutions