Induced Surfaces and Their Integrable Dynamics
Copyright policy )Induced Surfaces and Their Integrable Dynamics
A method is considered to induce surfaces in three‐dimensional (pseudo) Euclidean space via the solutions to two‐dimensional linear problems (20 LPs) and their integrable dynamics (deformations) via the 2 + 1‐dimensional nonlinear integrable equations associated with these 2D LPs. Coordinates Xi of the induced surfaces are defined as integrals over certain bilinear combinations of the wave functions ψ of these 20 LPs. General formulation as well as three concrete examples are considered. Some properties and features of such induction are discussed. Three‐dimensional Riemann spaces associated with 2 + 1‐dimensional nonlinear integrable equations are considered also.
- University of Salento Italy
Other completely integrable PDE, integrable dynamics, induced surfaces, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
Other completely integrable PDE, integrable dynamics, induced surfaces, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
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