FROM SOLITON EQUATIONS TO THEIR ZERO CURVATURE FORMULATION
A key property of classical (continuous) soliton systems is the fact that they correspond to nonlinear partial differential equations (NLPDE’s) which happen to be expressible as the integrability condition for a system of linear equations. Linear eigenvalue problems and associated t-evolutions have produced classes of soliton equations [1, 2] and have led to the disclosure of major integrability features (such as the existence of multisoliton solutions and infinite sequences of conserved quantities).
Unable to display preview. Download preview PDF.
- 3.Hietarinta, J. and Kruskal, M. D. (1992) Hirota forms for the six Painlevé equations from singularity analysis, in: Painlevé Transcendents—Their Asymptotics and Physical Applications, eds. D. Levi and P. Winternitz, Plenum Press, New York, pp. 175–186.Google Scholar
- 6.Hirota, R. (1976) Direct method of finding exact solutions of nonlinear evolution equations, in: Bäcklund Transformations, the Inverse Scattering Method, Solitons and their Applications, Springer Lecture Notes in Mathematics 515, ed. R.M. Miura, pp. 40–68.Google Scholar
- 8.Faá di Bruno (1857) Note sur une nouvelle formule de calcul différentiel, Quart. J. Pure Appl. Math. 1, pp. 359–360.Google Scholar
- 9.Gilson, C., Lambert, F., Nimmo, J., and Willox, R. (1996) On the combinatorics of the Hirota D-operators, Proc. Roy. Soc. Lond. A431, pp. 361–639.Google Scholar