Large-time existence results for the nonlocal NLS around ground state solutions

Hideo Takaoka, Toshihiro Tamaki

Type: Preprint

Publication Date: 2024-07-13

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2407.09784

Abstract

This paper discusses about solutions of the nonlocal nonlinear Schrodinger equation. We prove that the solution remains close to the orbit of the soliton for a large-time, if the initial data is close to the ground state solitons. The proof uses the hyperbolic dynamics near ground state, which exhibits properties of local structural stability of solutions with respect to the flows of the nonlocal nonlinear Schrodinger equation.

Locations

arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations	2018	Bo Yang Yong Chen
+	On the existence of infinite energy solutions for nonlinear Schrödinger equations	2009	Pablo Braz e Silva Lucas C. F. Ferreira Élder J. Villamizar‐Roa
+	Global Attractor of Nonlocal Nonlinear Schrödinger Equation on R	2016	Zhu Chao-sheng
+	An example of stable excited state on nonlinear Schrödinger equation with nonlocal nonlinearity	2011	Masaya Maeda Satoshi Masaki
+ PDF Chat	An example of stable excited state on nonlinear Schrödinger equation with nonlocal nonlinearity	2013	Masaya Maeda Satoshi Masaki
+ PDF Chat	Analyticity of Solutions to Nonlinear Schrödinger Equations	2001	Hidetake Uchida
+	Long-time asymptotic behavior for the nonlocal nonlinear Schrödinger equation in the solitonic region	2024	Gaozhan Li Yiling Yang Engui Fan
+ PDF Chat	LOCAL DYNAMICS NEAR UNSTABLE BRANCHES OF NLS SOLITONS	2013	Tai‐Peng Tsai
+	On asymptotic stability of moving ground states of the nonlinear Schrödinger equation	2014	Scipio Cuccagna
+ PDF Chat	Localized solitons of a ()-dimensional nonlocal nonlinear Schrödinger equation	2008	Ken-ichi Maruno Yasuhiro Ohta
+	Solitary waves and their critical behavior in a nonlinear nonlocal medium with power-law response	1998	Sumiyoshi Abe Akihiro Ogura
+ PDF Chat	Local existence, global existence, and scattering for the nonlinear Schrödinger equation	2016	Thierry Cazenave Ivan Naumkin
+ PDF Chat	Final state problem for the nonlocal nonlinear Schrödinger equation with dissipative nonlinearity	2019	Mamoru Okamoto Kota Uriya
+	Chaoticons described by nonlocal nonlinear Schrodinger equation	2016	Lanhua Zhong Yuqi Li Yong Chen Weiyi Hong Wei Hu Qi Guo
+ PDF Chat	A Universal Asymptotic Regime in the Hyperbolic Nonlinear Schrödinger Equation	2017	Mark J. Ablowitz Yi-Ping Ma Igor Rumanov
+	Long-time asymptotic behavior of the nonlocal nonlinear Schrödinger equation with finite density type initial data	2022	Shou‐Fu Tian Zhiqiang Li Jin‐Jie Yang
+	Global solutions and self‐similar solutions for coupled nonlinear Schrödinger equations	2017	Yaojun Ye
+	On Soliton Dynamics in Nonlinear Schrodinger Equations	2006	Zhou Gang Israel Michael Sigal
+	Internal vibrations of nonlocal nonlinear Schrödinger soliton	2009	E. V. Doktorov
+ PDF Chat	Local theory and long time behaviour of solutions of nonlinear Schrödinger equations	2022	Phan van Tin

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (0)

Action	Title	Year	Authors