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GAUGE TRANSFORMATION AND SOLITON SOLUTIONS FOR THE WHITHAM–BROER–KAUP SYSTEM IN THE SHALLOW WATER

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

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YAN ZHAN

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

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, and

BO TIAN

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

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https://doi.org/10.1142/S0217984912501643Cited by:2 (Source: Crossref)

Abstract

In the shallow-water studies, the Whitham–Broer–Kaup (WBK) system can be used to describe the propagation of the long waves. In this paper, based on the Lax pair of the WBK system, we derive the gauge transformation from the WBK system to the Ablowitz–Kaup–Newell–Segur (AKNS) system with the help of symbolic computation. Applying the Darboux transformation of the AKNS system, we obtain some soliton solutions of the WBK system. Those results might be useful in the investigations on the propagation of solitons in such situation as shallow water.

Keywords:

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