Asymptotic stability of solitons of the subcritical gKdV equations revisited

Yvan Martel, Frank Merle

Type: Article

Publication Date: 2004-10-02

Citations: 179

DOI: https://doi.org/10.1088/0951-7715/18/1/004

View Publication

Locations

Nonlinearity - View
HAL (Le Centre pour la Communication Scientifique Directe) - View

Similar Works

Action	Title	Year	Authors
+	Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations	2001	Yvan Martel Frank Merle Tai‐Peng Tsai
+	Linear Problems Related to Asymptotic Stability of Solitons of the Generalized KdV Equations	2006	Yvan Martel
+	Stability and asymptotic stability in the enrgy space of the sum of N solitons for subcritical GKdV equation	2002	Yvan Martel Franck Merle Tai‐Peng Tsai
+	Asymptotic Stability of Solitons¶for Subcritical Generalized KdV Equations	2001	Yvan Martel Frank Merle
+	Refined asymptotics around solitons for gKdV equations	2007	Yvan Martel Frank Merle
+	Asymptotic stability for the subcritical generalized Korteweg de Vries equations	2001	Yvan Martel Franck Merle
+	Asymptotic stability of solitons of the gKdV equations with general nonlinearity	2007	Yvan Martel Frank Merle
+	Stability and Asymptotic Stability for Subcritical gKdV Equations	2002	Yvan Martel Frank Merle Tai‐Peng Tsai
+ PDF Chat	Erratum to “Asymptotic Stability of Solitons for the Subcritical Generalized KdV Equations”	2002	Yvan Martel Frank Merle
+ PDF Chat	Multi-Soliton Solutions for the Supercritical gKdV Equations	2010	Vianney Combet
+	Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg—de Vries equation	2011	Yvan Martel Frank Merle
+ PDF Chat	Asymptotic stability of solitons of the gKdV equations with general nonlinearity	2007	Yvan Martel Frank Merle
+	Asymptotic N -soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations	2005	Yvan Martel
+ PDF Chat	Asymptotic stability of solitons for the Benjamin-Ono equation	2009	Carlos E. Kenig Yvan Martel
+	Refined asymptotics around solitons for gKdV equations	2008	Yvan Martel Frank Merle
+	Stability of soliton through interraction for subcritical GkdV	2005	Y. Martel Franck Merle
+	Instability of solitons - revisited, I: the critical generalized KdV equation	2017	Luiz Gustavo Farah Justin Holmer Svetlana Roudenko
+	Instability of solitons - revisited, I: the critical generalized KdV equation	2017	Luiz Gustavo Farah Justin Holmer Svetlana Roudenko
+ PDF Chat	Instability of solitons–revisited, I: The critical generalized KdV equation	2019	Luiz Gustavo Farah Justin Holmer Svetlana Roudenko
+	Construction of solutions to the subcritical gKdV equations with a given asymptotical behavior	2006	Raphaël Côte

Works That Cite This (173)

Action	Title	Year	Authors
+	On long-time behavior for solutions of the Gear–Grimshaw system	2023	Qihe Niang Deqin Zhou
+ PDF Chat	Nonexistence of small, odd breathers for a class of nonlinear wave equations	2016	Michał Kowalczyk Yvan Martel Claudio Muñoz
+ PDF Chat	Construction of a minimal mass blow up solution of the modified Benjamin–Ono equation	2016	Yvan Martel Didier Pilod
+	The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space	2018	Chulkwang Kwak Claudio Muñoz Felipe Poblete Juan C. Pozo
+ PDF Chat	Dynamics of KdV Solitons in the Presence of a Slowly Varying Potential	2011	Justin Holmer
+ PDF Chat	Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise	2009	Anne de Bouard Arnaud Debussche
+	Recent results for the Landau–Lifshitz equation	2021	André de Laire
+	Asymptotic stability of solitons for mKdV	2016	Pierre Germain Fabio Pusateri Frédéric Rousset
+ PDF Chat	Long time asymptotics of large data in the Kadomtsev–Petviashvili models	2024	Argenis J. Mendez Claudio Muñoz Felipe Poblete Juan C. Pozo
+ PDF Chat	Dynamics of Soliton-like Solutions for Slowly Varying, Generalized KdV Equations: Refraction versus Reflection	2012	Claudio Muñoz

Works Cited by This (23)

Action	Title	Year	Authors
+	Stability and Asymptotic Stability for Subcritical gKdV Equations	2002	Yvan Martel Frank Merle Tai‐Peng Tsai
+ PDF Chat	Asymptotic stability of solitary waves	1994	Robert L. Pego Michael I. Weinstein
+	Lyapunov stability of ground states of nonlinear dispersive evolution equations	1986	Michael I. Weinstein
+ PDF Chat	Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation	2005	Khaled El Dika
+	Model equations for long waves in nonlinear dispersive systems	1972	T. Brooke Benjamin Jerry L. Bona J. J. Mahony
+	Modulational Stability of Ground States of Nonlinear Schrödinger Equations	1985	Michael I. Weinstein
+ PDF Chat	Stabilité asymptotique des ondes solitaires de l'équation de Benjamin–Bona–Mahony	2003	Khaled El Dika
+	The emergence of solitons of the korteweg‐de vries equation from arbitrary initial conditions	1983	Wiktor Eckhaus Peter Schuur
+ PDF Chat	Stability of Blow-Up Profile and Lower Bounds for Blow-Up Rate for the Critical Generalized KdV Equation	2002	Yvan Martel Frank Merle
+	Asymptotic N -soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations	2005	Yvan Martel