A family of integrable evolution equations of third order |
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| Authors: | Matthew Babela |
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| Affiliation: | Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada |
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| 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. |
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| Keywords: | Integrable Equations Differential substitutions Krichever-Novikov equation 35Q58 37K05 37K10 37K25 |
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