On the relation between multifield and multidimensional integrable equations

Details On the relation between multifield and multidimensional integrable equations On the relation between multifield and multidimensional integrable equations

2000-11-21

arxiv.org/abs/nlin/0011039v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, 37K, LaTeX2E, submitted to Funct. Anal. Appl

Scientific paper

The new examples are found of the constraints which link the 1+2-dimensional and multifield integrable equations and lattices. The vector and matrix generalizations of the Nonlinear Schr\"odinger equation and the Ablowitz-Ladik lattice are considered among the other multifield models. It is demonstrated that using of the symmetries belonging to the hierarchies of these equations leads, in particular, to the KP equation and twodimensional analogs of the dressing chain, Toda lattice and dispersive long waves equations. In these examples the multifield equation and its symmetry have meaning of the Lax pair for the corresponding twodimensional equation under some compatible constraint between field variables and eigenfunctions.

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