Symbolic Computation of Conserved Densities for Systems of Nonlinear Evolution Equations

A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented inMathematica. The programcondens.mautomatically 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.mcan 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.