L Bombelli et al 1992 J. Phys. A: Math. Gen. 25 1309 doi:10.1088/0305-4470/25/5/032
Solvable systems of wave equations and non-Abelian Toda lattices
L Bombelli, W E Couch and R J Torrence
Show affiliationsRelates equivalence classes of coupled systems of N linear wave equations to motions of an N*N matrix dynamical systems, the two-dimensional non-Abelian Toda lattice. In particular, the correspondence is shown to relate those coupled systems of wave equations with progressing-wave general solutions to motions of the finite non-Abelian Toda lattice with free ends, generalizing a known result for the N=1 case. Some non-trivial motions of such Toda lattices are found, and the corresponding coupled wave equations and their progressing wave general solutions are given. Other consequences of the correspondence and possible application of the progressing waves are discussed.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
- MSC
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82C23 Exactly solvable dynamic models (See also 37K60)
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
- Subjects
- Dates
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Issue 5 (7 March 1992)
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Solvable systems of wave equations and non-Abelian Toda lattices
L Bombelli et al 1992 J. Phys. A: Math. Gen. 25 1309
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