On The Study Of Algebro-Geometric Solutions To Several Soliton Equations

In this paper, we focus on the algebro-geometric solutions of three 1+ 1-dimensional coupled soliton equations. According to the spectral problem and the auxiliary spectral problem, we introduce the theory of algebraic curve and elliptic vari-ables. Using the Abel-Jacobi coordinates which straighten out the time-space flows, the asymptotic properties of the meromorphic function (?) and Baker-Akhiezer function ψ1, and the algebro-geometric characters of hyperelliptic curve κ, we derive the algebro-geometric solutions of three 1+1-dimensional coupled soliton equations. It’s different from the Riemann-Jacobi inversion method.Chapter two and three, we derive the hierarchies of three 1+1-dimensional cou-pled soliton equations and corresponding evolutions of elliptic variables. In chapter four, we obtain explicit Riemann theta function solution of these three 1+1-dimensional coupled soliton equations using the Riemann-Jacobi inversion method. As a contact, we get the algebro-geometric solutions of coupled soliton equations using the asymp-totic properties of the meromorphic function (?) and Baker-Akhiezer functionψ1, and the algebro-geometric characters of hyperelliptic curve κ in chapter five. Chapter six, the bilinear form and N-soliton solutions are derived for a combined AKNS-CLL equation by Hirota approach...