Conservation laws for some nonlinear evolution equations which describe pseudo-spherical surfaces. (English) Zbl 1069.37058

Summary: The relation between pseudo-spherical surfaces and the inverse scattering method is exemplified for several evolution equations. Conservation laws for the latter ones are obtained using a geometrical property of these pseudo-spherical surfaces.


37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
58A10 Differential forms in global analysis
14Q10 Computational aspects of algebraic surfaces
35Q51 Soliton equations
53A05 Surfaces in Euclidean and related spaces
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
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