Resonant solutions of the non-linear Schrödinger equation with periodic potential

Authors

Arein Duaibes, College of Saint Benedict/Saint John's UniversityFollow
Yulia Karpeshina

Document Type

Article

Publication Date

7-24-2024

Disciplines

Mathematics | Non-linear Dynamics | Partial Differential Equations

Abstract

The goal is construction of stationary solutions close to non-trivial combinations of two plane waves at high energies for a periodic non-linear Schrödinger Equation in dimension two. The corresponding isoenergetic surface is described for any sufficiently large energy k2. It is shown that the isoenergetic surface corresponding to k2 is essentially different from that for the zero potential even for small potentials. We use a combination of the perturbative results obtained earlier for the linear case and a method of successive approximation.

Copyright Statement

© 2024 The Authors.

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

Recommended Citation

Duaibes A, Karpeshina Y. 2024. Resonant solutions of the non-linear Schrödinger equation with periodic potential. Nonlinearity 37(9): 095012. https://doi.org/10.1088/1361-6544/ad6127