Solitons for the (3+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equations in an optical fiber

2017 ◽  
Vol 109 ◽  
pp. 345-359 ◽  
Author(s):  
Gao-Fu Deng ◽  
Yi-Tian Gao
Keyword(s):  
Optical Fiber ◽  
Variable Coefficient ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Coupled Nonlinear Schrodinger Equations ◽  
Dimensional Variable

scholarly journals Quasi-periodic solutions of the coupled nonlinear Schrödinger equations

1995 ◽  
Vol 451 (1943) ◽  
pp. 685-700 ◽  
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Schrödinger Equations ◽  
Integrable Case ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Fibre Optics ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Coupled Nonlinear Schrodinger Equations

We consider travelling periodic and quasi-periodic wave solutions of a set of coupled nonlinear Schrödinger equations. In fibre optics these equations can be used to model single mode fibres under the action of cross-phase modulation, with weak birefringence. The problem is reduced to the ‘1:2:1’ integrable case of the two-particle quartic potential. A general approach for finding elliptic solutions is given. New solutions which are associated with two-gap Treibich-Verdier potentials are found. General quasi-periodic solutions are given in terms of two dimensional theta functions with explicit expressions for frequencies in terms of theta constants. The reduction of quasi-periodic solutions to elliptic functions is discussed.

Sign in / Sign up

Export Citation Format

Share Document