Bäcklund transformation of partial differential equations from the Painlevé-Gambier classification. II. Tzitzéica equation

DOI10.1063/1.532853zbMath0946.35086OpenAlexW2069256115WikidataQ115328317 ScholiaQ115328317MaRDI QIDQ4701840

Micheline Musette, Robert Conte, A. Michel Grundland

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532853

zbMATH Keywords

Darboux transformationBäcklund transformationTzitzéica equationHirota-Satsuma equationmatrix Lax pair

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) Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (7)

On Tzitéeica type nonlinear equations for multiple soliton solutions in nonlinear optics ⋮ Hyper-complex four-manifolds from the Tzitzéica equation ⋮ Analytic aspects of the Tzitzéica equation: blow-up analysis and existence results ⋮ A Bäcklund transformation for the Burgers hierarchy ⋮ A truncated Painlevé expansion associated with the Tzitzéica equation: consistency and general solution ⋮ Integrable motions of space curves in affine geometry ⋮ Exact soliton solutions for some nonlinear partial differential equations

Cites Work

• Nonlinear sigma model for the Dodd-Bullough equation
• The reduction problem and the inverse scattering method
• A class of 1-D gas flows soluble by the inverse scattering transform
• Bäcklund autotransformation for the equation \(u_{xt}=e^ u-e^{-2u}\)
• Darboux transformation and some multi-phase solutions of the Dodd-Bullough-Tzitzeica equation: \(U_{xt}=e^ U-e^{-2U}\).
• Self-dual Einstein spaces via a permutability theorem for the Tzitzeica equation.
• N-Soliton Solutions of Model Equations for Shallow Water Waves
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• A restricted Bäcklund transformation
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• Algorithmic method for deriving Lax pairs from the invariant Painlevé analysis of nonlinear partial differential equations
• The Painlevé property for partial differential equations
• On classes of integrable systems and the Painlevé property
• The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations
• SU(3) symmetry of the equations of unidimensional gas flow, with arbitrary entropy distribution
• Linearization and Painlevé property of Liouville and Cheng equations
• The gauge field copies and Backlund transformation
• A family of nonlinear Klein–Gordon equations and their solutions
• Bäcklund transformations for the sine–Gordon equations
• On an old article of Tzitzeica and the inverse scattering method
• On a shallow water wave equation
• The affinspharen equation. Moutard and Backlund transformations
• The Tzitzeica equation: A Bäcklund transformation interpreted as truncated Painlevé expansion
• Bäcklund transformation of partial differential equations from the Painlevé–Gambier classification. I. Kaup–Kupershmidt equation
• Bäcklund transformation and the Painlevé property
• The two-singular-manifold method: I. Modified Korteweg-de Vries and sine-Gordon equations
• The singular manifold method revisited
• Prolongation approach to Bäcklund transformation of Zhiber–Mikhailov–Shabat equation

This page was built for publication: Bäcklund transformation of partial differential equations from the Painlevé-Gambier classification. II. Tzitzéica equation