Stationary Veselov-Novikov equation and isothermally asymptotic surfaces in projective differential geometry

DOI10.1016/S0926-2245(99)00028-5zbMath0990.53008arXivmath/9805011OpenAlexW2085617542WikidataQ115337411 ScholiaQ115337411MaRDI QIDQ1807641

Evgeny V. Ferapontov

Publication date: 23 November 1999

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9805011

zbMATH Keywords

geometric Bäcklund transformationisothermally asymptotic surfacesLelieuvre representationstationary modified Veselov-Novikov equations

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Surfaces in Euclidean and related spaces (53A05) Projective differential geometry (53A20)

Related Items (10)

Surface theory in discrete projective differential geometry. I. A canonical frame and an integrable discrete Demoulin system ⋮ Bright solitons of the variants of the Novikov-Veselov equation with constant and variable coefficients ⋮ 2-soliton-solution of the Novikov-Veselov equation ⋮ Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation ⋮ Relationship between symmetries of the Tzitzéica equation and the Novikov-Veselov hierarchy ⋮ Projective differential geometry of higher reductions of the two-dimensional Dirac equation ⋮ A new exact solution and corresponding localized excitations of the \((2+1)\)-dimensional mKdV equation ⋮ Numerical study of blow-up and stability of line solitons for the Novikov–Veselov equation ⋮ Lie sphere geometry and integrable systems. ⋮ On a discretization of asymptotic nets

Cites Work

• Zur Differentialgeometrie der Flächen, die eine eingliedrige projektive Gruppe in sich gestatten, und über allgemeine Projektivrotationsflächen
• Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation
• Surfaces of Demoulin: Differential geometry, Bäcklund transformation and integrability
• Über die projektiv abwickelbaren isotherm-asymptotischen Flächen
• On generalized Loewner systems: Novel integrable equations in 2+1 dimensions
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