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Multi-lump solutions of KPI

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Abstract

A family of rational solutions of the Kadomtsev–Petviashvili I equation with N distinct peaks as \(|t| \rightarrow \infty \), is characterized in terms of the partitions of a positive integer N. This new approach leads to a complete classification of these N-lump solutions whose properties including the asymptotic location of the peaks are investigated using the Schur function associated with a given partition of N. Relationship between the geometric structures of the N-lump wave pattern and the Young diagram of the associated integer partition is explored.

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Acknowledgements

This project was partially supported by NSF Grant No. DMS-1911537.

Funding

This project was partially supported by NSF Grant No. DMS-1911537.

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  1. Department of Mathematics, University of Colorado, Colorado Springs, CO, 80918, USA

    Sarbarish Chakravarty

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  1. Sarbarish Chakravarty
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Correspondence to Sarbarish Chakravarty.

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Chakravarty, S. Multi-lump solutions of KPI. Nonlinear Dyn 112, 575–589 (2024). https://doi.org/10.1007/s11071-023-09044-y

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