Multidimensional Baker-Akhiezer functions and Huygens' Principle

Details Multidimensional Baker-Akhiezer functions and Huygens' Principle Multidimensional Baker-Akhiezer functions and Huygens' Principle

1999-03-09

arxiv.org/abs/math-ph/9903019v1

Physics

Mathematical Physics

35 pages, LATEX, 2 figures included in graphicx. Submitted to Comm.Math.Phys. (Dec. 1998)

Scientific paper

A notion of rational Baker-Akhiezer (BA) function related to a configuration of hyperplanes in C^n is introduced. It is proved that BA function exists only for very special configurations (locus configurations), which satisfy certain overdetermined algebraic system. The BA functions satisfy some algebraically integrable Schrodinger equations, so any locus configuration determines such an equation. Some results towards the classification of all locus configurations are presented. This theory is applied to the famous Hadamard's problem of description of all hyperbolic equations satisfying Huygens' Principle. We show that in a certain class all such equations are related to locus configurations and the corresponding fundamental solutions can be constructed explicitly from the BA functions.

Affiliated with

Also associated with

No associations

Rating

Multidimensional Baker-Akhiezer functions and Huygens' Principle 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 Multidimensional Baker-Akhiezer functions and Huygens' Principle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multidimensional Baker-Akhiezer functions and Huygens' Principle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-592933