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