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.
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