Elsevier

Physics Letters A

Volume 261, Issues 5–6, 18 October 1999, Pages 289-296
Physics Letters A

Quasi-periodic solutions of the 2+1 dimensional modified Korteweg–de Vries equation

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Abstract

A new 2+1 dimensional modified Korteweg–de Vries equation is proposed and decomposed into the first two members in the well-known Kaup–Newell hierarchy, which are reduced further into integrable ordinary differential equations in the invariant set produced by the stationary Kaup–Newell equation. The Abel–Jacobi coordinates are introduced to straighten out the flows, from which quasi-periodic solutions of the 2+1 dimensional modified Korteweg–de Vries equation are obtained in terms of the Riemann theta functions.

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Acknowledgements

Project 19671074 was supported by National Natural Science Foundation of China. One of the authors (X.G. Geng) would like to thank the Henan Science Foundation Committee of China for financial support.

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