Speaker : Prof. Baofeng Feng (Univ of Texas, Pan American)
Title : General bright-dark soliton solution to the continuous and discrete vector nonlinear Schrodinger equation
Time : 2014-06-12 (Thu) 15:00 - 16:00
Place : Lecture Hall, Inst. of Mathematics
Abstract: In the present talk, we consider general bright-dark soliton solution to the continuous and discrete vector nonlinear Schrodinger (NLS) 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 vector NLS equation. The conditions for the reality of this mixed-type soliton solution with all possible combinations of nonlinearities is elucidated. Regarding to the discrete vector NLS equation, we provide a general formula for bright-dark soliton solution in the form of pfaans. Then we prove this pfaan solution by Hirota's bilinear method.