| Abstract: |
| This talk is about the Riemann theta function solutions for the Ito hierarchy. The Lax pair of the Ito hierarchy is derived from a 4*4 matrix spectral problem using the zero-curvature equation and Lenard equations. Then, we introduce the corresponding tetragonal curve and its Riemann theta function through the characteristic polynomial of the Lax matrix, and also discuss the construction of three kinds of Abelian differentials. Building on the theory of tetragonal curves, we investigate algebro-geometric properties of Baker-Akhiezer functions and fundamental meromorphic functions. Finally, Riemann theta function solutions for the entire Ito hierarchy are derived via asymptotic analysis. |
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