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 second-order 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/s11232-007-0121-1
- arXiv:
- arXiv:0706.0075
- Bibcode:
- 2007TMP...153.1373A
- Keywords:
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- hierarchy of commuting vector fields;
- Riemann invariant;
- Dubrovin equations;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 17 p