Memoirs of the American Mathematical Society 1996; 88 pp; softcover Volume: 118 ISBN10: 0821804065 ISBN13: 9780821804063 List Price: US$39 Individual Members: US$23.40 Institutional Members: US$31.20 Order Code: MEMO/118/563
 Using commutation methods, the authors present a general formalism to construct Kortewegde Vries (KdV) and modified Kortewegde Vries (mKdV) \(N\)soliton solutions relative to arbitrary (m)KdV background solutions. As an illustration of these techniques, the authors combine them with algebrogeometric methods and Hirota's \(\tau\)function approach to systematically derive the (m)KdV \(N\)soliton solutions on quasiperiodic finitegap backgrounds. Readership Graduate students, research mathematicians, and theoretical physicists interested in soliton mathematics. Table of Contents  Introduction
 Quasiperiodic finitegap (m)KdVsolutions
 (m)KdVsoliton solutions on quasiperiodic finitegap backgrounds
 I. The single commutation method
 (m)KdVsoliton solutions on quasiperiodic finitegap 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)KdVsoliton solutions relative to general backgrounds
 Appendix E: Hyperelliptic curves and theta functions
 References
