Computer classification of integrable coupled KdV-like systems
Journal of Symbolic Computation
A new method for solving algebraic systems of positive dimension
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Triangular sets for solving polynomial systems: a comparative implementation of four methods
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Computing canonical representatives of regular differential ideals
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
On computer-assisted classification of coupled integrable equations
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Notes on triangular sets and triangulation-decomposition algorithms I: polynomial systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
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We show how the triangularization method of the second author can be successfully applied to the problem of classification of homogeneous coupled integrable equations. The classifications rely on the recent algorithm developed by the first author that requires solving 17 systems of polynomial equations. We show that these systems can be completely resolved in the case of coupled Korteweg-de Vries, Sawada-Kotera and Kaup-Kupershmidt—type equations.