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

- 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)

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

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

- 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)

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

Different criteria of integrability are used for the classification of equations (1): the existence of non-trivial symmetries (Fokas, 1980; Fujimoto & Watanabe, 1983), conservation laws (Abellanas & Galindo, 1983), prolongation structures (Leo et al., 1983). In this paper we shall describe a classification method based on the concept of formal integrability… (More)

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

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

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 verify the necessary integrability conditions which follow from the existence of a higher infinitesimal or Lie-Backlund [4] symmetry but often to find an explicit form of… (More)

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