Communications in Mathematical Physics

, Volume 149, Issue 2, pp 263–278 | Cite as

Solving the KP hierarchy by gauge transformations

  • Ling-Lie Chau
  • J. C. Shaw
  • H. C. Yen


We show that it is convenient to use “gauge” transformations (sometimes called explicit Bäcklund transformations) to generate new solutions for the KP hierarchy. Two particular kinds of gauge transformation operators, constructed out of the initial wave functions, are of fundamental importance in this approach. Through such gauge transformations, a very simple formula for the tau-function is obtained, encompassing and unifying all kinds of existing solutions. The corresponding free fermion representation and Baker functions for the new τ function can also be constructed.


Neural Network Statistical Physic Wave Function Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Ling-Lie Chau
    • 1
    • 2
  • J. C. Shaw
    • 3
  • H. C. Yen
    • 4
  1. 1.Department of PhysicsUniversity of CaliforniaDavis
  2. 2.Los Alamos National LaboratoryLos AlamosUSA
  3. 3.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan, R.O.C.
  4. 4.Department of PhysicsNational Tsing Hua UniversityHsinchuTaiwan, R.O.C.

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