Stability and instability of periodic travelling wave solutions for the critical Korteweg–de Vries and nonlinear Schrödinger equations

2009 ◽  
Vol 238 (6) ◽  
pp. 603-621 ◽  
Author(s):  
Jaime Angulo Pava ◽  
Fábio M. Amorin Natali
Keyword(s):  
Travelling Wave ◽  
Nonlinear Schrödinger Equations ◽  
Travelling Wave Solutions ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Stability And Instability ◽  
Periodic Travelling Wave ◽  
Nonlinear Schrodinger Equations ◽  
De Vries

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.

scholarly journals Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Dirk Hennig
Keyword(s):  
Fixed Point ◽  
Fixed Point Problem ◽  
Travelling Wave ◽  
Point Problem ◽  
Travelling Wave Solutions ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Periodic Travelling Wave ◽  
Discrete Nonlinear Schrödinger Equations

The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schrödinger equation (DNLS) on one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of interactions going beyond the usual nearest-neighbour interaction. The problem of the existence of travelling wave solutions is converted into a fixed point problem for an operator on some appropriate function space which is solved by means of Schauder’s Fixed Point Theorem.

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