A family of integrable evolution equations of third order

2016/08/10 by M. Babela, Babela, M., A. Odesskii +1
Mathematics · Physics and Astronomy · #35Q58 #37K05 #37K10 #37K25 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35Q58 #msc:37K05 #msc:37K10 #msc:37K25 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1608.03262

Latex, 8 pages

arxiv created 2016/08/10 · arxiv updated 2016/08/11

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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