Solutions to the KP hierarchy with an elliptic background

Saburo Kakei

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arXiv · 2310.11679

Solutions to the KP hierarchy with an elliptic background

Saburo Kakei

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Abstract

A class of "elliptic soliton" solutions of the Kadomtsev-Petviashvili hierarchy, which includes a determinantal solution of Li and Zhang, is described in terms of pseudo-differential operator formulation. In our approach, the Li-Zhang solution is obtained by repeatedly applying the Darboux transformation to a stationary solution. Real-valued solutions are discussed and various examples that display web-like patterns are presented.

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Saburo Kakei. 2023-10-18. Solutions to the KP hierarchy with an elliptic background. https://arxiv.org/abs/2310.11679

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