TY - JOUR
T1 - The mechanism of the polarizational mode instability in birefringent fiber optics
AU - Li, Yi A.
AU - Promislow, Keith
PY - 2000
Y1 - 2000
N2 - We show that the soliton solutions of the integrable Manakov equation exhibit an instability under arbitrarily small Hamiltonian perturbations. The instability arises from eigenvalues embedded in the essential spectrum of the associated linearized operators; these eigenvalues are dislodged by smooth perturbations. Specifically we consider perturbations which arise in fiber optics as a result of birefringence, including the so-called four-wave mixing term. Employing the Evans function and a Dirichlet expansion on the stable manifold of the linearized system, we obtain rigorous perturbation results and compute the stability diagram of the fast wave for all physical values of the birefringent parameters, using a novel numerical scheme derived from the Dirichlet expansion.
AB - We show that the soliton solutions of the integrable Manakov equation exhibit an instability under arbitrarily small Hamiltonian perturbations. The instability arises from eigenvalues embedded in the essential spectrum of the associated linearized operators; these eigenvalues are dislodged by smooth perturbations. Specifically we consider perturbations which arise in fiber optics as a result of birefringence, including the so-called four-wave mixing term. Employing the Evans function and a Dirichlet expansion on the stable manifold of the linearized system, we obtain rigorous perturbation results and compute the stability diagram of the fast wave for all physical values of the birefringent parameters, using a novel numerical scheme derived from the Dirichlet expansion.
KW - Dirichlet expansion
KW - Evans function
KW - Polarization mode instability
KW - Traveling waves
UR - http://www.scopus.com/inward/record.url?scp=0034347554&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0034347554&partnerID=8YFLogxK
U2 - 10.1137/S0036141099349966
DO - 10.1137/S0036141099349966
M3 - Article
AN - SCOPUS:0034347554
SN - 0036-1410
VL - 31
SP - 1351
EP - 1373
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 6
ER -