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Pitchfork bifurcation at line solitons for nonlinear Schr\'{o}dinger equations on the product space $\mathbb{R} \times \mathbb{T}$
- Publication Year :
- 2021
-
Abstract
- In this paper, we study the bifurcation problem from a line soliton for a stationary nonlinear Schr\"{o}dinger equation on the product space $\mathbb{R} \times \mathbb{T}$. We extend earlier results to a larger class of the nonlinearity in the equation. The salient point of our analysis relies on a lower bound of solution to the ``auxiliary equation'' and then on the application of the Crandall-Rabinowitz argument
- Subjects :
- Mathematics - Analysis of PDEs
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2103.05887
- Document Type :
- Working Paper