On the ill-posedness of the 5th-order Gardner equation

DOI10.1007/s40863-019-00150-7zbMath1435.37097arXiv1810.10434OpenAlexW2972546229WikidataQ89424788 ScholiaQ89424788MaRDI QIDQ2278989

Miguel A. Alejo, Eleomar jun. Cardoso

Publication date: 12 December 2019

Published in: São Paulo Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.10434

zbMATH Keywords

integrabilityill-posednessGardner equationbreather

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Ill-posed problems for PDEs (35R25) Soliton equations (35Q51) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (2)

Global solutions and stability properties of the 5th order Gardner equation ⋮ Dynamics of breathers in the Gardner hierarchy: universality of the variational characterization

Cites Work

• On the ill-posedness of the Gardner equation
• On the hierarchies of higher order mKdV and KdV equations
• Well-posedness and stability results for the Gardner equation
• On the ill-posedness of some canonical dispersive equations.
• A higher order modified Korteweg-de Vries equation
• The extended Korteweg-de Vries equation and the resonant flow of a fluid over topography
• Hamiltonian perturbation theory and water waves
• Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations
• Low regularity Cauchy problem for the fifth-order modified KdV equations on 𝕋
• Well-posedness and ill-posedness of the fifth order modifed KdV equation

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