Asymptotic integrability. (English) Zbl 0963.35167

Degasperis, A.; Procesi, M.

Degasperis, A. (ed.) et al., Symmetry and perturbation theory (SPT’98). Proceedings of the 2nd international workshop, Rome, Italy, December 16-22, 1998. Singapore: World Scientific. 23-37 (1999).

Summary: The multiscale expansion is shown to be a convenient tool to define asymptotic integrability up to order \(N\) of \(1+1\) dispersive nonlinear wave equations. Its connection with complete integrability, an algorithmic test and few examples are discussed. Approximate Lax pairs for asymptotically integrable PDEs are also provided.
For the entire collection see [Zbl 0944.00056].

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

Keywords:

approximate Lax pair; asymptotic integrability; complete integrability