Numerical study of self-focusing solutions to the Schrödinger-Debye system
Besse, Christophe ; Bidégaray, Brigitte
HAL, hal-00319989 / Harvested from HAL
Text on HAL
In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.
Publié le : 2001-07-05
Classification:  Nonlinear optics,  Schrödinger-like equations,  relaxation method,  split-step method,  self-focusing,  35Q55, 35Q60, 65M06, 65M70, 78A60,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] 
@article{hal-00319989,
     author = {Besse, Christophe and Bid\'egaray, Brigitte},
     title = {Numerical study of self-focusing solutions to the Schr\"odinger-Debye system},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00319989}
}

Besse, Christophe; Bidégaray, Brigitte. Numerical study of self-focusing solutions to the Schrödinger-Debye system. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00319989/