A family of integrable evolution equations of third order. Issue 1 (2nd January 2017) - Babela, Matthew; Odesskii, Alexandre
Abstract : We construct a family of integrable equations of the form vt = f ( v ; vx ; vxx ; vxxx ) such that f is a transcendental function in v ; vx ; vxx . This family is related to the Krichever-Novikov equation by a differential substitution. Our construction of integrable equations and the corresponding differential substitutions involves geometry of a family of genus two curves and their Jacobians.