D.E. Pelinovsky
Inertia Law for Spectral Stability of Solitary Waves in
Coupled Nonlinear Schrodinger Equations
Proc. Roy. Soc. Lond. A 461, 783-812 (2005)
Abstract:
Spectral stability analysis for solitary waves is developed in
context of the Hamiltonian system of coupled nonlinear
Schrodinger equations. The linear eigenvalue problem for a
non-self-adjoint operator is studied with two self-adjoint matrix
Schrodinger operators. Sharp bounds on the number and type of
unstable eigenvalues in the spectral problem are found from
inertia law for quadratic forms, associated with the two
self-adjoint operators. Symmetry-breaking stability analysis is
also developed with the same method.
Keywords:
STABILITY-INSTABILITY THEOREMS, COUPLED NONLINEAR SCHRODINGER EQUATIONS,
MATRIX SCHRODINGER OPERATORS, EIGENVALUES, EIGENFUNCTIONS,
SPECTRAL DECOMPOSITIONS