Y. Kodama and D. Pelinovsky

Spectral stability and time evolution of N-solitons in the KdV hierarchy

Journal of Physics A: Mathematical General 38, 6129-6140 (2005)

Abstract:
This paper concerns spectral stability and time evolution of N-solitons in the Korteweg-de Vries (KdV) hierarchy with mixed commuting time flows. Spectral stability problem is analysed by using a pair of self-adjoint operators with finite numbers of negative eigfenvalues. We show that the absence of unstable eigenvalues in the stability problem is related to the absence of negative eigenvalues of these operators in the constrained function spaces. Time evolution of N-solitons is uniquely characterized from the inverse scattering transform technique.

Keywords:
KDV HIERARCHY, CONSTRAINED VARIATIONAL PRINCIPLE, STABILITY OF SOLITARY WAVES, UNSTABLE EIGENVALUES, LINEARIZED HAMILTONIAN