Algebro-Geometric Solutions of a (2+1)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy - Xiaohong Chen (Advances in Mathematical Physics)
The (2+1)-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1+1)-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy. Then, based on the finite-order expansion of the Lax matrix, a hyperelliptic Riemann surface and Abel-Jacobi coordinates are introduced to straighten out the associated flows, from which the algebro-geometric solutions of the (2+1)-dimensional integrable equation are proposed by means of the Riemann θ functions.