TY - JOUR
TI - Phase plane Stackel potential dynamics of the Manakov system
AU - Polymilis, C
AU - Hizanidis, K
AU - Frantzeskakis, DJ
JO - Physical Review E
PY - 1998
VL - 58
TODO - 1
SP - 1112-1124
PB - AMER PHYSICAL SOC
SN - 2470-0045, 2470-0053
TODO - 10.1103/PhysRevE.58.1112
TODO - null
TODO - A wide class of traveling-wave solutions of the Manakov system of
coupled nonlinear Schrodinger equations is found to possess a potential
which leads to separability in the Stackel sense exhibiting two
integrals of motion, which facilitates a thorough investigation of this
system by nonlinear dynamics phase plane methods. On this basis,
specific types of nonlinear waves are identifred via a complete phase
space trajectory investigation. The topological features of the phase
space structure and the asymptotic behavior of the trajectory Families
involved are studied. Time domain analytical solutions are provided
involving hyperelliptic integrals and their series expressions of the
latter, in terms of the three elliptic integrals. Among the trajectory
families, solitary-type envelope solutions to the Manakov system are
easily identified on the basis of a limited number of parameters.
ER -