Bilinear methods and exact solutions

We have a long history of involvement in Hirota's bilinear formalism and its application to integrable systems.

In this approach, a transformation of the dependent variables reduce such systems to a form bilinear in the new dependent variables. Derivatives occur in special combinations called Hirota derivatives which facilitate finding classes of exact solutions, generally including the multi-soliton solutions.

There are also connections with representation theory.

Some publications
  1. C.X.Li, J.J.C.Nimmo, C.B.Hu and Gegenhasi, (2005) On an integrable modified (2+1)-dimensional Lotka-Volterra equation, J Math Anal Appl, (In press)
    X.B.Hu, C.X.Li, J.J.C.Nimmo and G.F.Yu (2005) An integrable symmetric (2+1)-dimensional Lotka-Volterra equation and a family of its exact solutions, J Phys A, 38, 197.
  2. C.Gilson, J.Hietarinta, J.J.C.Nimmo and Y.Ohta, (2003) Sasa-Satsuma higher-order nonlinear Schrodinger equation and its bilinearization and multisoliton solutions, Phys. Rev. E, 68, 016614.
  3. Y.Ohta, C. R.Gilson and J. J. C.Nimmo, (2001) A bilinear approach to a pfaffian self-dual Yang-Mills equation, Glasgow Mathematics Journal, 43A, 99--108.
  4. Gilson, C. R.; Nimmo, J. J. C. A direct method for dromion solutions of the Davey-Stewartson equations and their asymptotic properties Proc. Roy. Soc. London Ser. A 435 (1991), no. 1894, 339--357.
  5. Nimmo, J. J. C. Hall-Littlewood symmetric functions and the BKP equation. J. Phys. A 23 (1990), no. 5, 751--760.
  6. Nimmo, J. J. C. Wronskian determinants, the KP hierarchy and supersymmetric polynomials. J. Phys. A 22 (1989), no. 16, 3213--3221.