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Integrable equations of the dispersionless Hirota type

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posted on 06.08.2018, 13:33 by Lenos Hadjikos
Let u(x, y, t) be a function of three variables x, y, t. Equations of the dispersionless Hirota type have the form: F(uxx, uxy, uyy, uxt, uyt, utt) = 0. Familiar examples include the Boyer–Finley equation Uxx + Uyy = eutt, the potential form of the dispersionless Kadomtsev–Petviashvili (dKP) equation Uxt - ½u²xx = uyy, the dispersionless Hirota equation (α - β)euxy + (β – γ)euyt + (γ – α)eutx = 0, etc. We study integrability of such systems in the sense of the existence of infinitely many hydrodynamic reductions. The moduli space of integrable equations of the dispersionless Hirota type is proved to be 21-dimensional. In addition, it is shown that the action of the equivalence group Sp(6) on the moduli space has an open orbit.

Funding

Loughborough University, Mathematical Sciences Department.

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

© Lenos Hadjikos

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2009

Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.

Language

en

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