A. Yu. Zharkov

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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)
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)
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)
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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