Krichever-Novikov Equation

The partial differential equation

where

The special cases  and  can be reduced to the Korteweg-de Vries equation by a change of variables.

REFERENCES:

Krichever, I. M. and Novikov, S. P. "Holomorphic Bundles over Algebraic Curves, and Nonlinear Equations." Russ. Math. Surv. 35, 53-80, 1980. English translation of Uspekhi Mat. Nauk 35, 47-68, 1980.

Mokhov, O. I. "Canonical Hamiltonian Representation of the Krichever-Novikov Equation." Math. Notes 50, 939-945, 1991. English translation of Mat. Zametki 50, 87-96, 1991.

Novikov, D. P. "Algebraic-Geometric Solutions of the Krichever-Novikov Equation." Theoret. Math. Phys. 121, 1567-15773, 1999.

Sokolov, V. V. "Hamiltonian Property of the Krichever-Novikov Equation." Dokl. Akad. Nauk SSSR 277, 48-50, 1984.

Svinolupov, S. I.; Sokolov, V. V.; and Yamilov, R. I. "Bäcklund Transformations for Integrable Evolution Equations." Dokl. Akad. Nauk SSSR 271, 802-805, 1983. English translation of Sov. Math. Dokl. 28, 165-168, 1983.