| Full text | |
| Author(s): |
Corcho, Adan J.
;
Panthee, Mahendra
Total Authors: 2
|
| Document type: | Journal article |
| Source: | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 243, p. 17-pg., 2024-02-28. |
| Abstract | |
We consider the Cauchy problem associated to the focusing cubic nonlinear Schr & ouml;dinger equation posed on a two dimensional cylindrical domain R x T-& ell;. We prove that localized transverse perturbations of an especial one-parameter family of bound states solutions {u(omega,& ell;)}, omega > -pi(2)/& ell;(2) can be extended globally in time. On the other hand, we establish the existence of solution in the energy space H-1(R x T-& ell;), with non-critical mass, that blows-up in finite time under the hypothesis of no growth in time of the directional L-x(2)-norm of the solution when the periodic variable y is localized. We also prove that a family of bound states {u(omega,& ell;)} is not uniformly continuous from H-s(R x T-& ell;) into the space of continuous functions C([0,T]; H-s(R x T-& ell;)), whenever -1/2 <= s < 0, including the regularity s =-1/2 for the non-uniformly continuous flow, unlike to the case of focusing cubic nonlinear Schr & ouml;dinger equation on R. (AU) | |
| FAPESP's process: | 23/06416-6 - Nonlinear phenomena and dispersion |
| Grantee: | Mahendra Prasad Panthee |
| Support Opportunities: | Regular Research Grants |