On the hierarchies of higher order mKdV and KdV equations

Axel Grünrock

Type: Article

Publication Date: 2010-05-29

Citations: 36

DOI: https://doi.org/10.2478/s11533-010-0024-5

View Publication

Locations

Open Mathematics - View

Similar Works

Action	Title	Year	Authors
+	On the hierarchies of higher order mKdV and KdV equations	2009	Axel Gruenrock
+	Local Well and Ill Posedness for the Modified KdV Equations in Subcritical Modulation Spaces	2018	Mingjuan Chen Boling Guo
+ PDF Chat	Local well and ill posedness for the modified KdV equations in subcritical modulation spaces	2020	Mingjuan Chen Boling Guo
+	Well-posedness and ill-posedness of KdV equation with higher dispersion	2014	Li Yin Wei Yan
+	Global well-posedness for the fifth-order mKdV equation	2018	Xin Jun Gao
+	Complete Integrability of the Coupled KdV-mKdV System	2019	P.H.M. Kersten Joseph Krasil’shchik
+ PDF Chat	On local well-posedness and ill-posedness results for a coupled system of mkdv type equations	2020	Xavier Carvajal Liliana Esquivel Raphael Santos
+	Rogue waves on the periodic background in the high-order discrete mKdV equation	2023	Yanpei Zhen Jinbing Chen
+	Sharp well-posedness for a coupled system of mKdV type equations	2018	Xavier Carvajal Mahendra Panthee
+	A coupled <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si24.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo linebreak="goodbreak">+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional mKdV system and its nonlocal reductions	2020	Xiaoming Zhu
+	Complete integrability of the coupled KdV-mKdV system	2000	P.H.M. Kersten Joseph Krasil’shchik
+	Weak Continuity of Dynamical Systems for the KdV and mKdV Equations	2009	Shangbin Cui Carlos E. Kenig
+ PDF Chat	Weak continuity of dynamical systems for the KdV and mKdV equations	2010	Shangbin Cui Carlos E. Kenig
+	A numerical application of the decomposition method for the combined KdV–MKdV equation	2004	Dogˇan Kaya İbrahim E. İnan
+	Sharp ill-posedness results for the KdV and mKdV equations on the torus	2012	Luc Molinet
+ PDF Chat	On the Well-Posedness of the Defocusing mKdV Equation Below $L^{2}$	2017	Thomas Kappeler Jan-Cornelius Molnar
+	Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋	2003	J. Colliander M. Keel Gigliola Staffilani Hideo Takaoka Terence Tao
+	Well-posedness for the NLS hierarchy	2024	Joseph Adams
+ PDF Chat	Well-posedness for the NLS hierarchy	2024	Joseph Adams
+ PDF Chat	Local well-posedness for the periodic higher order KdV type equations	2011	Hiroyuki Hirayama

Works That Cite This (35)

Action	Title	Year	Authors
+ PDF Chat	On the extension of the frequency maps of the KdV and the KdV2 equations	2016	Thomas Kappeler Jan-Cornelius Molnar
+ PDF Chat	Well-Posedness for the Fifth Order KdV Equation	2012	Takamori Kato
+	Nonlinear stability of higher order mKdV breathers	2018	Miguel Á. Alejo Eleomar Cardoso
+	Parabolic smoothing effect and local well-posedness of fifth order semilinear dispersive equations on the torus	2017	Kotaro Tsugawa
+	On the ill-posedness of the 5th-order Gardner equation	2018	Miguel Á. Alejo Eleomar Cardoso
+	Multisolitons for the cubic NLS in 1-d and their stability	2020	Herbert Koch Daniel Tataru
+ PDF Chat	Conserved energies for the cubic nonlinear Schrödinger equation in one dimension	2018	Herbert Koch Daniel Tataru
+	Unique continuation principle for high order equations of Korteweg-de Vries type	2013	Pedro Isaza
+ PDF Chat	Control and stabilization of the periodic fifth order Korteweg-de Vries equation	2018	Cynthia Flores Derek L. Smith
+ PDF Chat	On the ill-posedness of the 5th-order Gardner equation	2019	Miguel Á. Alejo Eleomar Cardoso

Works Cited by This (42)

Action	Title	Year	Authors
+	None	2004	Axel Grünrock
+ PDF Chat	Inhomogeneous Strichartz estimates for the Schrödinger equation	2006	Mari Cruz Vilela
+	None	2005	Axel Grünrock
+	Regularity of solutions to the Schrödinger equation	1987	Per Sjölin
+	Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋	2003	J. Colliander M. Keel Gigliola Staffilani Hideo Takaoka Terence Tao
+ PDF Chat	Quadratic forms for the 1-D semilinear Schrödinger equation	1996	Carlos E. Kenig Gustavo Ponce Luis Vega
+	On the Hierarchy of the Generalized KdV Equations	1994	Carlos E. Kenig Gustavo Ponce Luis Vega
+	On the Cauchy Problem for the Zakharov System	1997	J. Ginibre Yoshio Tsutsumi G. Velo
+	On the ill-posedness of some canonical dispersive equations	2001	Carlos E. Kenig Gustavo Ponce Luis Vega
+	Quelques généralisations de l'équation de Korteweg-de Vries, II	1979	Jean‐Claude Saut