The Complex Hamilton Systems And Quasi-Periodic Solutions In The Hirota Equation

The Hirota equation is reduced to a pair of complex finite-dimensional Hamilton systems with Hamiltonians,which are proven to be completely integrable in the Liouville sense.It turns out that involutive solutions of the complex finite-dimensional Hamilton systems yield finite parametric solutions of the Hirota equation.The complex Novikov equation is given,which specifies a finite-dimensional invariant subspace of Hirota flows.From a Lax matrix of the complex finite-dimensional Hamilton systems,the Hirota flow is linearized to display its evolution behavior on the Jacobi variety of a Riemann surface.Based on the theory of algebra curve,the explicit quasi-periodic solutions of the Hirota equation is obtained with the help of the Riemann-Jacobi inversion.