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Symbolic Computation of Conserved Densities for Systems of Nonlinear Evolution Equations

Ünal Göktas
Organization: Wolfram Research, Inc.
Willy Hereman
Organization: Colorado School of Mines
Department: Department of Mathematical and Computer Sciences
Journal / Anthology

Journal of Symbolic Computation
Year: 1997
Volume: 24
Page range: 591-621

A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented in Mathematica. The program condens.m automatically carries out the lengthy symbolic computations for the construction of conserved densities. The code is tested on several well-known partial differential equations from soliton theory. For systems with parameters, condens.m can be used to determine the conditions on these parameters so that a sequence of conserved densities might exist. The existence of a large number of conservation laws is a predictor for integrability of the system.

*Mathematics > Calculus and Analysis > Differential Equations