Global solutions and stability properties of the 5th order Gardner equation

DOI10.1007/s10884-021-10022-4zbMath1527.35142arXiv1901.03350OpenAlexW3174137488WikidataQ115383123 ScholiaQ115383123MaRDI QIDQ6095773

Chulkwang Kwak, Miguel A. Alejo

Publication date: 8 September 2023

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.03350

zbMATH Keywords

stabilityintegrabilityglobal well-posednessGardner equationbreather

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for nonlinear higher-order PDEs (35G25) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (1)

Dynamics of breathers in the Gardner hierarchy: universality of the variational characterization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local well-posedness for the fifth-order KdV equations on \(\mathbb{T}\)
• Nonlinear stability of MKdV breathers
• Global well-posedness and I method for the fifth order Korteweg-de Vries equation
• On the ill-posedness of the Gardner equation
• On the hierarchies of higher order mKdV and KdV equations
• Uniform well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation
• Local well-posedness and a priori bounds for the modified Benjamin-Ono equation
• Local well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces
• Lax pairs and higher order models for water waves
• An instability property of the nonlinear Schrödinger equation on \(S^d\)
• Global well-posedness of the KP-I initial-value problem in the energy space
• On the Cauchy problem for higher-order nonlinear dispersive equations
• On the fifth-order KdV equation: Local well-posedness and lack of uniform continuity of the solution map
• Low regularity solutions of two fifth-order KdV type equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• On the Cauchy problem for periodic KdV-type equations
• Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
• Two singular dynamics of the nonlinear Schrödinger equation on a plane domain
• Nonlinear stability of Gardner breathers
• Local well-posedness for the KdV hierarchy at high regularity
• Unconditional uniqueness for the modified Korteweg-de Vries equation on the line
• Breathers and the dynamics of solutions in KdV type equations
• Strichartz estimates for dispersive equations and solvability of the Kawahara equation
• On the ill-posedness of some canonical dispersive equations.
• A higher order modified Korteweg-de Vries equation
• The initial-boundary value problem for the Kawahara equation on the half-line
• Local well-posedness of the fifth-order KdV-type equations on the half-line
• On the ill-posedness of the 5th-order Gardner equation
• Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers
• Nonlinear stability of 2-solitons of the sine-Gordon equation in the energy space
• Rough solutions of the fifth-order KdV equations
• On finite energy solutions of the KP-I equation
• A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order
• On the variational structure of breather solutions. I: Sine-Gordon equation
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• Ill-Posedness Issues for the Benjamin--Ono and Related Equations
• The Modified Korteweg-de Vries Equation
• Bilinearization of Nonlinear Evolution Equations. III. Bäcklund Transformations of Higher-Order Korteweg-de Vries Equations
• Well-Posedness for the Fifth Order KdV Equation
• Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation
• The extended Korteweg-de Vries equation and the resonant flow of a fluid over topography
• On the Dynamics of Zero-Speed Solutions for Camassa–Holm-Type Equations
• Global well-posedness of the Benjamin–Ono equation in low-regularity spaces
• Hamiltonian perturbation theory and water waves
• Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
• Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations
• Higher-Order Nonlinear Dispersive Equations
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• Non-Existence of Solutions for the Periodic Cubic NLS below ${L}^{{2}}$
• Instability in nonlinear Schrödinger breathers
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• A bilinear estimate with applications to the KdV equation
• Generation of solitons and breathers in the extended Korteweg–de Vries equation with positive cubic nonlinearity
• Low regularity Cauchy problem for the fifth-order modified KdV equations on 𝕋
• A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces
• Well-posedness and ill-posedness of the fifth order modifed KdV equation
• Well-posedness for the fifth-order KdV equation in the energy space

This page was built for publication: Global solutions and stability properties of the 5th order Gardner equation