PHASE PLANE STACKEL POTENTIAL DYNAMICS OF THE MANAKOV SYSTEM

A wide class of traveling-wave solutions of the Manakov system of coup led nonlinear Schrodinger equations is found to possess a potential wh ich leads to separability in the Stackel sense exhibiting two integral s of motion, which facilitates a thorough investigation of this system by nonlinear dynamics phase plane methods. On this basis, specific ty pes of nonlinear waves are identifred via a complete phase space traje ctory investigation. The topological features of the phase space struc ture and the asymptotic behavior of the trajectory Families involved a re studied. Time domain analytical solutions are provided involving hy perelliptic integrals and their series expressions of the latter, in t erms of the three elliptic integrals. Among the trajectory families, s olitary-type envelope solutions to the Manakov system are easily ident ified on the basis of a limited number of parameters.