Date: Monday, December 04, 2017
Location: 1866 East Hall (4:00 PM to 5:00 PM)
Title: Darboux transformation for vector nonlinear Schrodinger equation (vNLSE) on the nonvanishing background
Abstract: As we well known that, the Darboux transformation is a powerful method to generate some interesting exact solutions from some trivial solutions for the integrable equations. For instance, through the zero solution of vNLSE, the multisoliton solutions can be constructed. In recent years, there are lots of works which focus on generating the exact solutions by the plane wave seed solution (genus zero solution). Some physical solutionsthe Akhmediev breather, KM breather, rogue wave solution, dark soliton, brightdark soliton and so on can be readily constructed. In this talk, we give the Darboux transformations for integrable vNLSE with different types. Furthermore, we give the exact solutions for the vNLSE on the nonvanishing background by some analysis on the formulas. Here, we stress that the inverse scattering theory of vNLSE for the nonvanishing background was not solved completely under the general plane wave background. But by applying the Darboux transformation, the exact solutions and relationship with the discrete spectrum are clear, which means that the discrete spectrum part of inverse scattering theory is solved.
Files:
Speaker: Liming Ling
Institution: South China University of Technology
Event Organizer: Thomas Bothner and Guilherme Silva bothner@umich.edu, silvag@umich.edu
