Nonlinear Waves Seminar - Xudan Luo
| Event Description: Xudan Luo, The inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions. The nonlocal nonlinear Schrödinger (NLS) equation was introduced and shown to be integrable. In this talk, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is shown to be well posed for certain potentials such that analyticity properties of eigenfunctions and scattering data are established. The inverse scattering problem is developed via a left-right Riemann-Hilbert problem in terms of a uniform variable. Finally, the Cauchy problem for nonlocal NLS equation with nonzero boundary conditions is formulated and the methods to find pure soliton solutions are discussed, which, in tun, leads to an explicit 1-soliton solution. |
| Location Information: ÌýÌý() 1111 Engineering DR Boulder, CO Room:Ìý226: Applied Math Conference Room |
| Contact Information: Name: Ian Cunningham Phone: 303-492-4668 Email: amassist@colorado.edu |