D.E. Pelinovsky and V.M. Rothos
Evans function for the AKNS problem with
"Mathematical and numerical aspects of wave propagation: WAVES 2003",
Proceedings of the Sixth International Conference on Mathematical and Numerical
Aspects of Wave Propagation Held at Jyvaskyla, Finland, 30 June - 4 July 2003, Eds.
G.C. Cohen, E. Heikkola, P. Joly, P. Neittaanmaki, Springer, 729-734 (2003)
We study renormalizations of the Evans function for the
AKNS spectral problem on a real line with algebraically decaying potentials.
We show that the Evans function may have pole
singularities at embedded eigenvalues of the essential spectrum,
which are related to algebraically decaying eigenfunctions.
Stability of algebraic solitons in the initial-value problem for the
modified KdV equation is studied with the renormalized Evans function.
EVANS FUNCTION, EMBEDDED EIGENVALUES,
ESSENTIAL SPECTRUM OF LINEAR OPERATORS,
ALGEBRAIC SOLITONS, AKNS SPECTRAL PROBLEM,
MODIFIED KORTEWEG-DE VRIES EQUATION.