COMPUTER ALGEBRA, SYMMETRY ANALYSIS AND INTEGRABILITY OF NONLINEAR EVOLUTION EQUATIONS

Vladimir P. Gerdt
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Vladimir P. Gerdt: Laboratory of Computing Techniques and Automation, Joint Institute for Nuclear Research, Head Post Office P.O. Box 79, 141980 Dubna, Russia

International Journal of Modern Physics C (IJMPC), 1993, vol. 04, issue 02, 279-286

Abstract: A computer algebra-aided symmetry approach to investigating integrability of polynomial-nonlinear evolution equations in one-temporal and one-spatial dimensions is presented. The approach is based on verifying the existence of higher conservation laws and symmetries. If the equations contain arbitrary numerical parameters, the problem of selection of all the integrable cases is reduced to the solving polynomial equations in those parameters. The Gröbner basis technique is used in order to simplify and to solve such polynomial systems which typically have infinitely many solutions.

Date: 1993
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DOI: 10.1142/S012918319300029X

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