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

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

2005-04-13

arxiv.org/abs/nlin/0504029v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages

Scientific paper

10.1088/0305-4470/38/27/003

This paper concerns spectral stability and time evolution of $N$-solitons in the KdV hierarchy with mixed commuting time flows. Spectral stability problem is analyzed by using a pair of self-adjoint operators with finite numbers of negative eigenvalues. 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.

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