Back to Search
Start Over
Stability of Algebraic Solitons for Nonlinear Schrödinger Equations of Derivative Type: Variational Approach
- Source :
- Annales Henri Poincaré. 23(12):4249-4277
- Publication Year :
- 2022
- Publisher :
- Springer Nature, 2022.
-
Abstract
- We consider the following nonlinear Schrödinger equation of derivative type: \begin{equation} i \partial_t u + \partial_x^2 u +i |u|^{2} \partial_x u +b|u|^4u=0 , \quad (t,x) \in \mathbb{R}\times\mathbb{R}, \ b \in \mathbb{R}. \end{equation} If $b=0$, this equation is a gauge equivalent form of well-known derivative nonlinear Schrödinger (DNLS) equation. The soliton profile of the DNLS equation satisfies a certain double power elliptic equation with cubic-quintic nonlinearities. The quintic nonlinearity in the equation only affects the coefficient in front of the quintic term in the elliptic equation, so the additional nonlinearity is natural as a perturbation preserving soliton profiles of the DNLS equation. If $b>-\frac{3}{16}$, the equation has algebraic solitons as well as exponentially decaying solitons. In this paper we study stability properties of solitons by variational approach, and prove that if $b<br />26 pages, 1 figure. Final version
Details
- Language :
- English
- ISSN :
- 14240637
- Volume :
- 23
- Issue :
- 12
- Database :
- OpenAIRE
- Journal :
- Annales Henri Poincaré
- Accession number :
- edsair.doi.dedup.....9458ce293b5bbe0a76b92ac7b7d05a57