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Solvable systems of wave equations and non-Abelian Toda lattices

L Bombelli, W E Couch and R J Torrence

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Relates 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

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

03.65.Ca Formalism

03.65.Ge Solutions of wave equations: bound states

MSC

82C23 Exactly solvable dynamic models (See also 37K60)

82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs

35L05 Wave equation

37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

Subjects

Quantum information and quantum mechanics

Statistical physics and nonlinear systems

Dates

Issue 5 (7 March 1992)



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