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Solutions to the KP hierarchy with an elliptic background
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Solutions to the KP hierarchy with an elliptic background
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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.
Forward citations
Cited by 3 Pith papers
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Asymptotic Equivalence Between Quasi-Grammian and Quasi-Wronskian $N$-Soliton Solutions of the Anti-Self-Dual Yang-Mills Equation
Quasi-Grammian and quasi-Wronskian N-soliton solutions of the ASDYM/Yang equation are asymptotically equivalent up to a constant matrix factor, with explicit N-soliton phase shifts.
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Degenerate Addition Formulas of the KP Hierarchy and Applications
The KP tau-function addition formula is shown to degenerate to a Wronskian identity, linking vertex-operator and Darboux solutions and yielding a new theta addition formula.
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Integrability and transformations in the bilinear method: An introduction
A pedagogical review of Hirota's bilinear method connecting the three-soliton condition with Hirota integrability, Backlund transformations, and vertex-operator transformations of tau functions; no new results are proved.
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