Now showing items 1-10 of 22
Vector shock soliton and the Hirota bilinear method
The Hirota bilinear method is applied to find an exact shock soliton solution of the system reaction-diffusion equations for n-component vector order parameter, with the reaction part in form of the third order polynomial, ...
On a 2+1-dimensional Whitham-Broer-Kaup system: A resonant NLS connection
It is established that the Whitham-Broer-Kaup shallow water system and the "resonant" nonlinear Schrödinger equation are equivalent. A symmetric integrable 2+1-dimensional version of the Whitham-Broer-Kaup system is ...
Multi-wave and rational solutions for nonlinear evolution equations
(De Gruyter, 2010-08)
Nonlinear evolution equations always admit multi-soliton and rational solutions. The Burgers equation is used as an example, and the exp-function method is used to eluciadte the solution procedure.
Exact and explicit solutions to nonlinear evolution equations using the division theorem
In this paper, we show the applicability of the first integral method, which is based on the ring theory of commutative algebra, to the regularized long-wave Burgers equation and the Gilson-Pickering equation under a ...
Nonlinear integral equations for Bernoulli's free boundary value problem in three dimensions
In this paper we present a numerical solution method for the Bernoulli free boundary value problem for the Laplace equation in three dimensions. We extend a nonlinear integral equation approach for the free boundary ...
Variations on a theme of q-oscillator
(IOP Publishing, 2015-07-01)
We present several ideas in the direction of physical interpretation of q- and f-oscillators as nonlinear oscillators. First we show that an arbitrary one-dimensional integrable system in action-angle variables can be ...
A note on the (G′/G)-expansion method again
We report an observation on two recent analytic methods; the (G′/G)-expansion method and the simplest equation method. © 2010 Elsevier Inc. All rights reserved.
The Ablowitz-Ladik lattice system by means of the extended (G′ / G)-expansion method
We analyzed the Ablowitz-Ladik lattice system by using the extended (G′ / G)-expansion method. Further discrete soliton and periodic wave solutions with more arbitrary parameters are obtained. We observed that some previously ...
Comment on: "Application of Exp-function method for (3+1 )-dimensional nonlinear evolution equations" [Comput. Math. Appl. 56 (2008) 14511456]
We show that Boz and Bekir [A. Boz, A. Bekir, Application of Exp-function method for (3+1)-dimensional nonlinear evolution equations, Comput. Math. Appl. 56 (2008) 14511456] obtained some incorrect solutions for the equations ...
Filamentary structures of the cosmic web and the nonlinear Schrödinger type equation
(IOP Publishing, 2011)
We show that the filamentary type structures of the cosmic web can be modeled as solitonic waves by solving the reaction diffusion system which is the hydrodynamical analogous of the nonlinear Schrödinger type equation. ...