General bright-dark soliton solution to the continuous and discrete vector nonlinear Schroedinger equation

Baofeng Feng (University of Texas-Pan American)

Friday 8th August, 2014 15:00-16:00 Maths 509

Abstract

In the present talk, we consider general bright-dark soliton solution to the continuous and
discrete vector nonlinear Schroedinger (vNLS) equation of all possible combinations of nonlinearities including all-focusing, all-defocusing and mixed types. By using the KP-hierarchy
reduction method based on the Sato-theory, we construct a general bright-dark soliton solution
expresses in term of Gram-type determinants for the continuous vNLS equation. The
conditions for the reality of this mixed-type soliton solution with all possible combinations
of nonlinearities is elucidated.

Regarding to the discrete vNLS equation, we provide a general formula for bright-dark
soliton solution in the form of pfaffians. Then we prove this pfaffian solution by Hirota’s
bilinear method.

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