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

Khater, A. H.; Callebaut, D. K.; Sayed, S. M.

J. Geom. Phys. 51, No. 3, 332-352 (2004).

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.

MSC:

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

Keywords:

conservation laws; nonlinear evolution equations; geometrical methods; inverse scattering method; differential forms; solitons; hyper-surfaces

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