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arXiv · 2103.05887

Pitchfork bifurcation at line solitons for nonlinear Schrödinger equations on the product space $\mathbb{R} \times \mathbb{T}$

Takafumi Akahori·Yakine Bahri·Slim Ibrahim·Hiroaki Kikuchi
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Abstract

In this paper, we study the bifurcation problem from a line soliton for a stationary nonlinear Schrödinger 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

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Takafumi Akahori, Yakine Bahri, Slim Ibrahim, Hiroaki Kikuchi. 2022-01-18. Pitchfork bifurcation at line solitons for nonlinear Schrödinger equations on the product space $\mathbb{R} \times \mathbb{T}$. https://arxiv.org/abs/2103.05887

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