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(m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions
Fritz Gesztesy, University of Missouri-Columbia, MO, and Roman Svirsky, University of Tennessee, Knoxville, TN
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Memoirs of the American Mathematical Society
1996; 88 pp; softcover
Volume: 118
ISBN-10: 0-8218-0406-5
ISBN-13: 978-0-8218-0406-3
List Price: US$39
Individual Members: US$23.40
Institutional Members: US$31.20
Order Code: MEMO/118/563
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Using commutation methods, the authors present a general formalism to construct Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) \(N\)-soliton solutions relative to arbitrary (m)KdV background solutions. As an illustration of these techniques, the authors combine them with algebro-geometric methods and Hirota's \(\tau\)-function approach to systematically derive the (m)KdV \(N\)-soliton solutions on quasi-periodic finite-gap backgrounds.

Readership

Graduate students, research mathematicians, and theoretical physicists interested in soliton mathematics.

Table of Contents

  • Introduction
  • Quasi-periodic finite-gap (m)KdV-solutions
  • (m)KdV-soliton solutions on quasi-periodic finite-gap backgrounds
  • I. The single commutation method
  • (m)KdV-soliton solutions on quasi-periodic finite-gap backgrounds
  • II. The double commutation method
  • Appendix A: Single commutation methods
  • Appendix B: Double commutation methods
  • Appendix C: Lax pairs, \(\tau\)-functions and Bäcklund transformations
  • Appendix D: (m)KdV-soliton solutions relative to general backgrounds
  • Appendix E: Hyperelliptic curves and theta functions
  • References
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