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arXiv · 1608.03262

A family of integrable evolution equations of third order

M. Babela·A. Odesskii
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Abstract

We construct a family of integrable equations of the form $v_t=f(v,v_x,v_{xx},v_{xxx})$ such that $f$ is a transcendental function in $v,v_x,v_{xx}$. 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.

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M. Babela, A. Odesskii. 2016-08-10. A family of integrable evolution equations of third order. https://arxiv.org/abs/1608.03262

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