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- Vladimir P. Gerdt, A. Yu. Zharkov
- J. Symb. Comput.
- 1990

- Vladimir P. Gerdt, A. Yu. Zharkov
- ISSAC
- 1990

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)

- A. Yu. Zharkov
- J. Symb. Comput.
- 1993

- Vladimir P. Gerdt, N. V. Khutornoy, A. Yu. Zharkov
- ISSAC
- 1990

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)

- Vladimir P. Gerdt, A. B. Shabat, S. I. Svinolupov, A. Yu. Zharkov
- EUROCAL
- 1987

- Vladimir P. Gerdt, A. Yu. Zharkov
- EUROCAL
- 1987

- Vladimir P. Gerdt, N. V. Khutornoy, A. Yu. Zharkov
- ISSAC
- 1991

In this paper we apply computer-aided symmetry approach [1]-[2] 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 [3]. Symmetry approach allows not only to… (More)

- Vladimir P. Gerdt, A. B. Shvachka, A. Yu. Zharkov
- J. Symb. Comput.
- 1985

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.

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