New Construction of Algebro-Geometric Solutions to the Modified Kadomtsev-Petviashvili Hierarchy
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 $\psi_1(P)\psi_2(P^*)$ on $X\times \mathbb{R}^3$ and Dubrovin-type equations for auxiliary divisors.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2014
- DOI:
- arXiv:
- arXiv:1411.3401
- Bibcode:
- 2014arXiv1411.3401Z
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 42 pages. arXiv admin note: substantial text overlap with arXiv:1410.7516