Publication Date
2008
Journal or Book Title
arXiv Preprint
Abstract
Asymptotic stability of small solitons in one dimension is proved in the framework of a discrete nonlinear Schrödinger equation with septic and higher power-law nonlinearities and an external potential supporting a simple isolated eigenvalue. The analysis relies on the dispersive decay estimates from Pelinovsky & Stefanov (2008) and the arguments of Mizumachi (2008) for a continuous nonlinear Schr¨odinger equation in one dimension. Numerical simulations suggest that the actual decay rate of perturbations near the asymptotically stable solitons is higher than the one used in the analysis.
Recommended Citation
Kevrekidis, PG, "Asymptotic stability of small solitons in the discrete nonlinear Schrödinger equation in one dimension" (2008). arXiv Preprint. 1143.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1143