Model equation of the theory of solitons
Abstract
We consider the hierarchy of integrable (1+2)dimensional equations related to the Lie algebra of vector fields on the line. We construct solutions in quadratures that contain n arbitrary functions of a single argument. A simple equation for the generating function of the hierarchy, which determines the dynamics in negative times and finds applications to secondorder spectral problems, is of main interest. Considering its polynomial solutions under the condition that the corresponding potential is regular allows developing a rather general theory of integrable (1+1)dimensional equations.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 October 2007
 DOI:
 10.1007/s1123200701211
 arXiv:
 arXiv:0706.0075
 Bibcode:
 2007TMP...153.1373A
 Keywords:

 hierarchy of commuting vector fields;
 Riemann invariant;
 Dubrovin equations;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 17 p