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

B. Enriquez; A. Yu. Orlov; V. N. Rubtsov

doi:10.1088/0266-5611/12/3/005

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arXiv · solv-int/9510002

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

B. Enriquez·A. Yu. Orlov·V. N. Rubtsov

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Abstract

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, $τ$-functions).

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BibTeX RIS

B. Enriquez, A. Yu. Orlov, V. N. Rubtsov. 1995-10-11. Dispersionful analogues of Benney's equations and $N$-wave systems. https://doi.org/10.1088/0266-5611%2F12%2F3%2F005

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