Global Dynamics Below Excited Solitons for the Non-Radial NLS with Potential

Author

Satoshi Masaki
Jason Murphy, Missouri University of Science and TechnologyFollow
Jun Ichi Segata

Abstract

We consider the global dynamics of solutions to the 3d cubic nonlinear Schrödinger equation in the presence of an external potential, in the setting in which the equation admits both ground state solitons and excited solitons at small mass. We prove that small mass solutions with energy below that of the excited solitons either scatter to the ground states or grow their H1-norm in time. In particular, we give an extension of the result of Nakanishi [30] from the radial to the non-radial setting.

Recommended Citation

S. Masaki et al., "Global Dynamics Below Excited Solitons for the Non-Radial NLS with Potential," Indiana University Mathematics Journal, vol. 73, no. 3, pp. 1097 - 1205, Indiana University Mathematics Journal, Jan 2024.

The definitive version is available at https://doi.org/10.1512/iumj.2024.73.9893

Department(s)

Mathematics and Statistics

Comments

Japan Society for the Promotion of Science, Grant JP21H00991

International Standard Serial Number (ISSN)

0022-2518

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Indiana University Mathematics Journal, All rights reserved.

Publication Date

01 Jan 2024