Classification of Monge-Ampère equations with two variables

Boris Kruglikov

Type: Article

Publication Date: 1999-01-01

Citations: 11

DOI: https://doi.org/10.4064/-50-1-179-194

Abstract

This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegen

Locations

Banach Center Publications - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Differential invariants of generic hyperbolic Monge-Ampère equations	2007	Michal Marvan A. M. Vinogradov V. A. Yumaguzhin
+	Equivalence and characteristic connections of the Monge-Ampere equations	1997	Дмитрий Васильевич Туницкий
+	On the contact linearization of Monge-Ampere equations	1996	Дмитрий Васильевич Туницкий
+	Differential invariants of generic parabolic Monge-Ampere equations	2008	Diego Catalano Ferraioli A. M. Vinogradov
+	Application of equivalence method to Monge-Amp\`ere equations: Elliptic case	2013	Moheddine Imsatfia
+	Application of equivalence method to Monge-Ampère equations: Elliptic case	2013	Moheddine Imsatfia
+	Symmetries and contact transformations of Monge–Ampère equations	2010	Alexei Kushner Valentin Lychagin Vladimir Rubtsov
+	Monge-Ampére equations and characteristic connection functors	2001	Дмитрий Васильевич Туницкий
+	On Contact Equivalence of Monge-Ampère Equations to Linear Equations with Constant Coefficients	2009	Alexei Kushner
+	THE CAUCHY PROBLEM FOR HYPERBOLIC MONGE-AMPÈRE EQUATIONS	1994	Дмитрий Васильевич Туницкий
+ PDF Chat	On the classification of symmetry reductions for the (1+3)-dimensional Monge–Ampère equation	2020	В. М. Федорчук В. І. Федорчук
+	Lectures on Geometry of Monge–Ampère Equations with Maple	2019	Alexei Kushner Valentin Lychagin Jan Slovák
+	CLASSIFICATION OF MIXED TYPE MONGE–AMPERE EQUATIONS	1994	Alexey Kushner
+ PDF Chat	Contact-equivalence problem for linear hyperbolic equations	2006	Oleg I. Morozov
+ PDF Chat	Homogeneous Bäcklund transformations of hyperbolic Monge–Ampère systems	2002	Jeanne N. Clelland
+	On some categories of Monge-Ampère systems of equations	2009	Dmitry Vasilievich Tunitsky
+	Classification of Monge–Ampeère Equations	2009	Alexei Kushner
+	Contact Equivalence Problem for Linear Hyperbolic Equations	2004	Oleg I. Morozov
+	Homogeneous Backlund transformations of hyperbolic Monge-Ampere systems	2001	Jeanne N. Clelland
+	Symplectic and contact Lie algebras with an application to Monge-Ampere equations	1997	Boris Kruglikov

Works That Cite This (11)

Action	Title	Year	Authors
+ PDF Chat	Differential invariants of generic hyperbolic Monge-Ampère equations	2007	Michal Marvan A. M. Vinogradov V. A. Yumaguzhin
+	Contact Relative Differential Invariants for Non Generic Parabolic Monge-Ampère Equations	2008	R. Alonso Blanco Gianni Manno Fabrizio Pugliese
+	Transformation of hyperbolic Monge-Ampére equations into linear equations with constant coefficients	2008	Alexei Kushner
+	Scalar dierential invariants of symplectic Monge-Ampère equations	2011	A. M. Vinogradov R. Caccioppoli Monte S. Angelo
+ PDF Chat	INVARIANTS OF PSEUDOGROUP ACTIONS: HOMOLOGICAL METHODS AND FINITENESS THEOREM	2006	Boris Kruglikov Valentin Lychagin
+ PDF Chat	Scalar differential invariants of symplectic Monge-Ampère equations	2011	Alessandro De Paris A. M. Vinogradov
+ PDF Chat	Monge–Ampère geometry and vortices	2024	Lewis Napper Ian Roulstone Vladimir Rubtsov Martin Wolf
+	Contact linearization of nondegenerate Monge-Ampère equations	2008	Alexei Kushner
+	A Contact Linearization Problem for Monge-Ampère Equations and Laplace Invariants	2008	Alexei Kushner
+	On Contact Equivalence of Monge-Ampère Equations to Linear Equations with Constant Coefficients	2009	Alexei Kushner

Works Cited by This (8)

Action	Title	Year	Authors
+	Leçons sur l'intégration des équations aux dérivées partielles du second ordre à deux variables indépendantes:	1896	Édouard Goursat
+	Lectures on Differential Geometry.	1966	J. R. Vanstone S. Sternberg
+ PDF Chat	A classification of Monge-Ampère equations	1993	Valentin Lychagin V. Rubtsov I. V. Chekalov
+	CONTACT GEOMETRY AND NON-LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS	1979	Valentin Lychagin
+	On Xm-forming sets of eigenvectors	1955	J. Haantjes
+	Complex Analytic Coordinates in Almost Complex Manifolds	1957	August Newlander Louis Nirenberg
+	Theory of Vector-Valued Differential Forms	1956	Alfred Frölicher Albert Nijenhuis
+ PDF Chat	Symplectic geometry of mixed type equations	1995	Alexei Kushner