New Construction of Algebro-Geometric Solutions to the Modified Kadomtsev-Petviashvili Hierarchy

2014/11/13 by Peng Zhao, Zhao, Peng, Engui Fan +1
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1411.3401

Abstract

We extend Gesztesy-Holden's method to 2+1 dimensional case to obtain a unified construction to the algebro-geometric solutions of the whole modified Kadomtsev-Petviashvili (mKP) hierarchy. Our tools include the relations between solutions of the Gerdjikov-Ivanov (GI) and mKP hierarchy, the Baker-Akhiezer functions in 2+1 dimensions, a special function ψ₁(P)ψ₂(P^*) on X× ℝ³ and Dubrovin-type equations for auxiliary divisors.

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