Numerical simulation of blow-up solutions of the vector nonlinear Schroedinger equation

We present numerical simulations of blow-up solutions of the vector nonlinear Schroedinger equation, which arises as the subsonic limit of the vectorial Zakharov system in plasma physics. In the course of our calculations, we observed the phenomenon of splitting of the solution profile. To capture the structure of the solution, we developed a new dynamic mesh refinement method based on the iterative grid distribution method introduced by Ren and Wang [J. Comput. Phys. 159, 246 (2000)]. We also applied this method to study the time dispersion nonlinear Schroedinger equation that describes the propagation of ultrashort pulses in a dispersive medium