Singular Solitons and Indefinite Metrics

Details Singular Solitons and Indefinite Metrics Singular Solitons and Indefinite Metrics

2011-03-13

arxiv.org/abs/1103.2505v2

Physics

Mathematical Physics

LaTex, 23 pages, 3 figures, essentially extended version, proof of convergence theorem was added

Scientific paper

The singular real second order 1D Schrodinger operators are considered here with such potentials that all local solutions near singularities to the eigenvalue problem are meromorphic for all values of the spectral parameter. All algebro geometrical or "singular finite-gap" potentials satisfy to this condition. A Spectral Theory is constructed here for the periodic and rapidly decreasing cases in the special classes of functions with singularities and indefinite inner product. It has a finite number of negative squares if the unimodular Bloch multipliers are fixed in the periodic case, and in the rapidly decreasing case. The time dynamics provided by the KdV hierarchy preserves this number. The right analog of Fourier Transform for the Riemann Surfaces preserving remarkable multiplicative properties of the ordinary (i.e. genus zero) Fourier Transform based on the standard exponential basis, leads to such operators as it was shown in our previous works.

Affiliated with

Also associated with

No associations

Rating

Singular Solitons and Indefinite Metrics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Singular Solitons and Indefinite Metrics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singular Solitons and Indefinite Metrics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-233697