Symplectic Structures and Volume Elements in the Function Space for the Cubic Schrodinger Equation

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

20 pages, AMS-TEX

Scientific paper

We consider various trace formulas for the cubic Schrodinger equation in the space of infinitely smooth functions subject to periodic boundary conditions. The formulas relate conventional integrals of motion to the periods of some Abelian differentials (holomorphic one-forms) on the spectral curve. We show that the periods of Abelian differentials are global coordinates on the moduli space of spectral curves. The exterior derivatives of the holomorphic one-forms are the basic and higher symplectic structures on the phase space. We write explicitly these symplectic structures in $QP$ coordinates. We compute the ratio of two symplectic volume elements in the infinite genus limit.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Symplectic Structures and Volume Elements in the Function Space for the Cubic Schrodinger Equation 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 Symplectic Structures and Volume Elements in the Function Space for the Cubic Schrodinger Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symplectic Structures and Volume Elements in the Function Space for the Cubic Schrodinger Equation will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-672815

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.