A Numerical Scheme for the Simulation of Blow-up in the Nonlinear Schrödinger Equation
S. Jiménez, I. M. Llorente, A. Mancho, V. M. Pérez-García, L. Vázquez
Applied Mathematics and Computation, 134, 271-291 (2003).
Pérez García, Victor M..
We present a self-adaptive multigrid version of a conservative finite difference scheme useful for the study of collapse processes in nonlinear Schrödinger equations (NLSEs). As an example we study the character of the focusing singularity of the two-dimensional critical NLSE.