252 research outputs found
The Prolongation Problem for the Heavenly Equation
We provide an exact regular solution of an operator system arising as the
prolongation structure associated with the heavenly equation. This solution is
expressed in terms of operator Bessel coefficients.Comment: 9 pages, Proc. SIGRAV Conference (Bari 1998
Integrable nonlinear field equations and loop algebra structures
We apply the (direct and inverse) prolongation method to a couple of
nonlinear Schr{\"o}dinger equations. These are taken as a laboratory field
model for analyzing the existence of a connection between the integrability
property and loop algebras. Exploiting a realization of the Kac-Moody type of
the incomplete prolongation algebra associated with the system under
consideration, we develop a procedure with allows us to generate a new class of
integrable nonlinear field equations containing the original ones as a special
case.Comment: 13 pages, latex, no figures
Equations of the reaction-diffusion type with a loop algebra structure
A system of equations of the reaction-diffusion type is studied in the
framework of both the direct and the inverse prolongation structure. We find
that this system allows an incomplete prolongation Lie algebra, which is used
to find the spectral problem and a whole class of nonlinear field equations
containing the original ones as a special case.Comment: 16 pages, LaTex. submitted to Inverse Problem
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