scholarly journals Spike vector solutions for some coupled nonlinear Schrödinger equations

2015 ◽  
Vol 36 (4) ◽  
pp. 2205-2227 ◽  
Author(s):  
Huirong Pi ◽  
Shuangjie Peng

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.


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