# American Institute of Mathematical Sciences

July  2017, 37(7): 4091-4108. doi: 10.3934/dcds.2017174

## Stability of Hasimoto solitons in energy space for a fourth order nonlinear Schrödinger type equation

 School of Mathematics and Big Data, Foshan University, Foshan, Guangdong 528000, China

* Corresponding author: Zhong Wang.

Received  December 2015 Revised  April 2016 Published  April 2017

Fund Project: This work is supported by the China National Natural Science Foundation under grant number 11571381.

In this article we investigate the nonlinear stability of Hasimoto solitons, in energy space, for a fourth order Schrödinger equation (4NLS) which arises in the context of the vortex filament. The proof relies on a suitable Lyapunov functional, at the $H^2$ level, which allows us to describe the dynamics of small perturbations. This stability result is also extended to Sobolev spaces $H^m$ for all $m∈\mathbb{Z}_+$ by employing the infinite conservation laws of 4NLS.

Citation: Zhong Wang. Stability of Hasimoto solitons in energy space for a fourth order nonlinear Schrödinger type equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 4091-4108. doi: 10.3934/dcds.2017174
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