scholarly journals Travelling Wave Solutions for the KdV-Burgers-Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
S. M. Sayed ◽  
O. O. Elhamahmy ◽  
G. M. Gharib
Keyword(s):  
Travelling Wave ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Travelling Wave Solutions ◽  
Schrödinger Equations ◽  
Constant Gaussian Curvature ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Pseudospherical Surfaces ◽  
Nonlinear Schrodinger Equations

We use the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudospherical surfaces for the KdV-Burgers-Kuramoto and nonlinear Schrödinger equations with constant Gaussian curvature−1. Travelling wave solutions for the above equations are obtained by using a sech-tanh method and Wu's elimination method.

TRAVELLING WAVE SOLUTIONS TO THE COUPLED DISCRETE NONLINEAR SCHRÖDINGER EQUATIONS

2005 ◽  
Vol 19 (13) ◽  
pp. 2129-2143 ◽  
Author(s):  
CHAO-QING DAI ◽  
JIE-FANG ZHANG
Keyword(s):  
Elliptic Function ◽  
Integrable Model ◽  
Travelling Wave ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Jacobian Elliptic Function ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Discrete Nonlinear Schrödinger Equations

In this paper, we have utilized the extended Jacobian elliptic function approach to construct seven families of new Jacobian elliptic function solutions for the coupled discrete nonlinear Schrödinger equations. When the modulus m → 1 or 0, some of these obtained solutions degenerate to the soliton solutions (the moving bright-bright and dark-dark solitons), the solitonic solutions and the trigonometric function solutions. This integrable model possesses the moving solitons because there is no PN barrier to block their motion in the lattice. We also find that some solutions in differential-difference equations (DDEs) are essentially identical to the continuous cases, while some solutions such as sec-type and tan-type in differential-difference models present different properties.

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