Dispersionful analogues of Benney's equations and $N$-wave systems

Details Dispersionful analogues of Benney's equations and $N$-wave systems Dispersionful analogues of Benney's equations and $N$-wave systems

1995-10-11

arxiv.org/abs/solv-int/9510002v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, latex, no figures

Scientific paper

10.1088/0266-5611/12/3/005

We recall Krichever's construction of additional flows to Benney's hierarchy, attached to poles at finite distance of the Lax operator. Then we construct a ``dispersionful'' analogue of this hierarchy, in which the role of poles at finite distance is played by Miura fields. We connect this hierarchy with $N$-wave systems, and prove several facts about the latter (Lax representation, Chern-Simons-type Lagrangian, connection with Liouville equation, $\tau$-functions).

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