Some Geometric Aspects of Integrability of Differential Equations in Two Independent Variables

Keywords

Integrable system, Mathematics, Conservation law, Infinitesimal, Homogeneous space

References

• Pseudospherical surfaces and evolution equationsShiing-Shen Chern, Keti Tenenblat — 1986
• What Is IntegrabilityВ. Е. Захаров, Ercolani, N M, Calogero, Francesco — 1991
• Soliton equations and differential geometryChuu-Lian Terng — 1997
• Applications of Lie Groups to Differential EquationsOlver, Peter J. 1952- — 1986
• Hamiltonian methods in the theory of solitonsL. D. Faddeev, Leon A. Takhtajan — 1987
• Conservation laws for nonlinear evolution equationsJ. A. Cavalcante, Keti Tenenblat — 1988
• Poisson actions and scattering theory for integrable systemsChuu-Lian Terng, Karen Uhlenbeck — 1997
• The symmetry approach to the classification of non-linear equations. Complete lists of integrable systemsА. В. Михайлов, A. B. Shabat, R. I. Yamilov — 1987
• Darboux coordinates and Liouville-Arnold integration in loop algebrasM. R. Adams, J. Harnad, J. Hurtubise — 1992
• Transformations of Manifolds and Applications to Differential EquationsKeti Tenenblat — 1998
• Equations of the inverse problem, backlund transformations, and the theory of connectionsA. K. Rybnikov — 1999
• A Harry Dym class of bihamiltonian evolution equationsL. Abellanas, Alberto Galindo — 1985
• Soliton equations and pseudospherical surfacesRyu Sasaki — 1979
• Evolutionary equations with nontrivial Lie - Bäcklund groupN. Kh. Ibragimov, A. B. Shabat — 1980
• Inverse scattering method with variable spectral parameterSergey Burtsev, В. Е. Захаров, А. В. Михайлов — 1987
• Pseudo-spherical Surfaces and Integrability of Evolution EquationsEnríque G. Reyes — 1998
• Classification of third order integrable evolution equationsRafael Hernández Heredero, В. В. Соколов, S. I. Svinolupov — 1995
• Conservation laws and Calapso-Guichard deformations of equations describing pseudo-spherical surfacesEnríque G. Reyes — 2000
• Weak nonlocalities in evolution equationsS. I. Svinolupov, В. В. Соколов — 1990
• On Differential Equations Describing Pseudo-Spherical SurfacesNiky Kamran, Keti Tenenblat — 1995

Cited by

• The Soliton Content of the Camassa-Holm and Hunter-Saxton EquationsEnríque G. Reyes — 2002
• Intrinsic Formulation of Geometric Integrability and Generation of Conservation LawsPAUL BRACKEN — 2007
• Geometric Integrability of the Camassa-Holm Equation. IIRafael Hernández Heredero, Enríque G. Reyes — 2011
• Correspondence theorems for hierarchies of equations of pseudo-spherical typeEnríque G. Reyes — 2002
• On generalized Bäcklund transformations for equations describing pseudo-spherical surfacesEnríque G. Reyes — 2003
• The NLS- equation and its SL(2,R) structureQing Ding — 2000
• Exact solutions for some nonlinear evolution equations which describe pseudo-spherical surfacesA. H. Khater, D. K. Callebaut, S. M. Sayed — 2006
• A new integrable two-component system with cubic nonlinearityJunfeng Song, Changzheng Qu, Zhijun Qiao — 2011
• Scalar second-order evolution equations possessing an irreducible sl2-valued zero-curvature representationMichal Marvan — 2002
• On formal integrability of evolution equations and local geometry of surfacesMikhail V. Foursov, Peter J. Olver, Enríque G. Reyes — 2001
• Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equationsEnríque G. Reyes — 2002
• Remarks on Undecidability, Incompleteness and the Integrability ProblemEnríque G. Reyes — 2010
• Equations of Pseudo-Spherical Type (After S.S. Chern and K. Tenenblat)Enríque G. Reyes — 2011
• Nonlocal symmetries and the Kaup–Kupershmidt equationEnríque G. Reyes — 2005
• The Modified Camassa–Holm EquationPrzemysław Górka, Enríque G. Reyes — 2010
• Geometric Integrability of the Camassa–Holm EquationEnríque G. Reyes — 2002
• A Novikov equation describing pseudo‐spherical surfaces, its pseudo‐potentials, and local isometric immersionsIgor Leite Freire, Rodrigo da Silva Tito — 2021
• Breakdown of pseudospherical surfaces determined by the Camassa-Holm equationIgor Leite Freire — 2024
• Existence and uniqueness of periodic pseudospherical surfaces emanating from Cauchy problemsNilay Duruk Mutlubaş, Igor Leite Freire — 2023
• Local Isometric Immersions and Breakdown of Manifolds Determined by Cauchy Problems of the Degasperis–Procesi EquationIgor Leite Freire — 2023

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