Computation of quasi-periodic solutions to the nonlinear Schrodinger equation

时   间：  2023-03-31 14:00 — 16:00

In this talk, we will show our recent work on the computation of  the quasi-periodic solutions to the nonlinear Schrodinger equation. By use of Hirota's bilinear method and theta function, we transform the problem of solving this kind of solutions into an over-determined nonlinear algebraic system, which can be formulated as a nonlinear least square problem and solved by the Levenberg-Marquardt method. The numerical experiments show that, in some cases the quasi-periodic solutions behave like breathers while in some other cases, they may act like periodic bright solitons and homoclinic solutions which can be taken as rogue waves when their amplitudes are much larger than their backgrounds. Besides, the quasi-periodic solutions may have singularities in some cases. Such kind of singular quasi-periodic solutions can be used to describe the phenomena of wave collapse.