Correspondence theorems for hierarchies of equations of pseudo-spherical type

Keywords

Mathematics, Type (biology), Pure mathematics, Algebra over a field, Mathematical analysis

References

• Some Geometric Aspects of Integrability of Differential Equations in Two Independent VariablesEnríque G. Reyes — 2000
• Symmetries and conservation laws for differential equations of mathematical physicsA. Bocharov, В. Н. Четвериков, S. Duzhin — 1999
• Pseudospherical surfaces and evolution equationsShiing-Shen Chern, Keti Tenenblat — 1986
• Soliton Equations and Hamiltonian SystemsL. A. Dickey — 2003
• Review: L. D. Faddeev and L. A. Takhtajan, Hamiltonian methods in the theory of solitonsR. K. Dodd — 1988
• Applications of Lie Groups to Differential EquationsOlver, Peter J. 1952- — 1986
• A global version of the inverse problem of the calculus of variationsFloris Takens — 1979
• The Geometrical Study of Differential EquationsLeslie, Joshua A., Joshua A. Leslie — 2001
• Hamiltonian methods in the theory of solitonsL. D. Faddeev, Leon A. Takhtajan — 1987
• 2-manifolds of constant curvature, 3-parameter isometry groups and bäcklund transformations☆Michael Crampin, Luke Hodgkin, David Robinson — 1980
• Transformations of solutions for equations and hierarchies of pseudo-spherical typeEnríque G. Reyes — 2003
• Scattering and inverse scattering for first order systemsRichard Beals, Ronald R. Coifman — 1984
• Isometric immersions of Riemannian manifoldsHideki Omori — 1967
• On generalized Bäcklund transformations for equations describing pseudo-spherical surfacesEnríque G. Reyes — 2003
• Transformations of Manifolds and Applications to Differential EquationsKeti Tenenblat — 1998
• Classically solvable field theory modelFernando Lund — 1978
• Tau-functions and dressing transformations for zero-curvature affine integrable equationsL. A. Ferreira, J. Luis Miramontes, J. Sánchez-Guillén — 1996
• The cauchy problem for pfaffian systemsRobert B. Gardner — 1969
• Soliton equations and pseudospherical surfacesRyu Sasaki — 1979
• Pseudo-spherical Surfaces and Integrability of Evolution EquationsEnríque G. Reyes — 1998

Cited by

• Third-order differential equations and local isometric immersions of pseudospherical surfacesTarcísio Castro Silva, Niky Kamran — 2015
• Second-order equations and local isometric immersions of pseudo-spherical surfacesNabil Kahouadji, Niky Kamran, Keti Tenenblat — 2013
• INTEGRABLE SYSTEMS DETERMINED BY DIFFERENTIAL FORMS FOR MOVING FRAMES ON IMMERSED SUBMANIFOLDSPaul Bracken — 2008
• Transformations of solutions for equations and hierarchies of pseudo-spherical typeEnríque G. Reyes — 2003
• Fifth-order evolution equations describing pseudospherical surfacesV.P. Gomes Neto — 2010
• Equations of Pseudo-Spherical Type (After S.S. Chern and K. Tenenblat)Enríque G. Reyes — 2011
• Fourth order evolution equations which describe pseudospherical surfacesDiego Catalano Ferraioli, Keti Tenenblat — 2014
• Third order differential equations describing pseudospherical surfacesTarcísio Castro Silva, Keti Tenenblat — 2015
• Uma classe de equações diferenciais de terceira ordem que descrevem superfícies pseudo-esféricasT. C. Silva — 2014
• Local isometric immersions of pseudo-spherical surfaces and kth order evolution equationsNabil Kahouadji, Niky Kamran, Keti Tenenblat — 2017
• 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
• A class of third order quasilinear partial differential equations describing spherical or pseudospherical surfacesDiego Catalano Ferraioli, Tarcísio Castro Silva — 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
• A look on equations describing pseudospherical surfacesIgor Leite Freire — 2025
• A Class of Third Order Quasilinear Partial Differential Equations Describingspherical or Pseudospherical SurfacesDiego Catalano Ferraioli, Tarcísio Castro Silva — 2023
• Global and blow-up solutions for a non-local integrable equation with applications to geometryNilay Duruk Mutlubaş, Igor Leite Freire — 2025
• Intrinsic geometry and wave-breaking phenomena in solutions of the Camassa-Holm equationIgor Leite Freire — 2023
• A class of third order partial differential equations describing spherical or pseudospherical surfacesDiego Catalano Ferraioli, Tarcísio Castro Silva — 2023

Related papers

• Maslov-type Indices for Iterations of Hyperbolic Closed Characteristics on Positive-type HypersurfacesTianqing An — 2005
• NEAR DIFFERENCE SETS OF TYPE 2Guozhen Shen — 1995
• Szasz-Type Operators which Preserves e0 and e2N. Srinivasa Rao, Abdul Wafi, Deepmala Deepmala — 2019
• Some Special Type of CI-AlgebrasPulak Sabhapandit, Kulajit Pathak — 2018
• Weighted Weak-type Estimates for Multilinear Commutators of Fractional Integrals on Spaces of Homogeneous TypeOsvaldo Gorosito, Gladis Pradolini, Oscar Salinas — 2007
• Hodge type of subvarieties of ℙn of small degreesH�l�ne Esnault — 1990
• A Picard type theorem for quasiregular mappings of R^n into n-manifolds with many endsIlkka Holopainen, Seppo Rickman — 1992
• A Perron-type theorem for nonautonomous difference equations with nonuniform behaviorHailong Zhu, Can Zhang, Yongxin Jiang — 2015
• Marcinkiewicz integral on hardy spacesYong Ding, Shanzhen Lu, Quigying Xue — 2002
• A Liouville-type theorem for very weak solutions of nonlinear partial differential equationsAlberto Fıorenza — 1997