# KP solitons and total positivity for the Grassmannian

@article{Kodama2011KPSA, title={KP solitons and total positivity for the Grassmannian}, author={Yuji Kodama and Lauren K. Williams}, journal={Inventiones mathematicae}, year={2011}, volume={198}, pages={637-699} }

Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that one can use the Wronskian method to construct a soliton solution to the KP equation from each point of the real Grassmannian $$Gr_{k,n}$$Grk,n. More recently, several authors (Biondini and Chakravarty, J Math Phys 47:033514, 2006; Biondini and Kodama, J. Phys A Math Gen 36:10519–10536…

## 104 Citations

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Combinatorics of KP Solitons from the Real Grassmannian

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Given a point A in the real Grassmannian, it is well-known that one can construct a soliton solution u A (x,y,t) to the KP equation. The contour plot of such a solution provides a tropical…

Fully resonant soliton interactions in the Whitham–Broer–Kaup system based on the double Wronskian solutions

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With the aim of exploring whether the (1+1)-dimensional coupled nonlinear evolution equations admit abundant soliton interactions, like the cases in the Kadomtsev–Petviashvili II equation, we in this…

Total positivity, Grassmannian and modified
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A rectangular matrix is called totally positive, if all its minors are positive. A point of a real Grassmanian manifold $G_{l,m}$ of $l$-dimensional subspaces in $\mathbb R^m$ is called strictly…

Total positivity for Grassmannians and amplituhedra

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Author(s): Karp, Steven Neil | Advisor(s): Williams, Lauren K. | Abstract: Total positivity is the mathematical study of spaces and their positive parts, which can have interesting combinatorial…

Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system

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Numerical studies of the KP line-solitons

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