We use the symmetry approach to establish an efficient program in REDUCE for verifying necessary integrability conditions for polynomial-nonlinear evolution equations and systems in one-spatial and one-temporal dimensions. These conditions follow from the existence of higher infinitesimal symmetries and conservation law densities. We briefly consider the… (More)
The investigation of the problem of integrability of polynomial-nonlinear evolution equations, in particular, verifying the existence of the higher symmetries and conservation laws can often be reduced to the problem of finding the exact solution of a complicated system of nonlinear algebraic equations. It is remarkable that these algebraic equations can be… (More)
In this paper we apply computer-aided symmetry approach - to investigation of the following eighth-parametric system of two coupled nonlinear Schrodinger equations where a~, &,-y~, 6~ (i = 1,2)-real parameters. The complete integrability of (1) at 71 = 72 and & = 62 have been studied by another method in . Symmetry approach allows not only to… (More)
The application of computer algebra for classification of integrable non-linear evolution equations is discussed. Algorithms for testing conditions of formal integrability, to calculate the Lie-B/icklund symmetries and conservation law densities are developed and implemented on the basis of the computer algebra system PL/1-mRMhC.