Abstract

Considerable interest centres at the present time on the problem of approximating the dynamical motion of solitons by an underlying discrete dynamical system. It has recently been demonstrated that the dynamics of N-solitons of the Nonlinear Schrodinger Equation (NSE) is quite well approximated by Complex Toda Lattice Equations (CTLE) in the limit of large separation of almost identical solitons with arbitrary phases [1-4]. The Lagrangian method proposed in [1, 2] is a direct reduction procedure which does not depend on the integrability of the original equations, and is applicable in principle to any Hamiltonian system having sufficiently well behaved solitary waves. Here it is shown that a Lagrangian theory similar to that of Gorshkov-Ostrowski [5] reduces a large class of nonintegrable Hamiltonian wave systems to a double Toda lattice in the limit of large separations of identical solitary pulses, generalising the results of [1-4] quite considerably.

© 1998 Optical Society of America