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N-soliton solutions and asymptotic analysis for a Kadomtsev–Petviashvili–Schrödinger system for water waves

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Abstract

Under investigation in this paper is a Kadomtsev–Petviashvili–Schrödinger system, which describes the long waves in shallow water. Integrability study has been made through the Painlevé test. Via the Hirota method, the bilinear form and N-soliton solutions are obtained with an auxiliary variable. Collision of two solitons is found to be elastic by means of the asymptotic analysis. From the graphical descriptions of the two- and three-soliton solutions, it is found that both the bright and dark solitons collide with one another without any change in the physical quantities except for some small phase shifts during the process of each collision.

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Authors and Affiliations

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

    Yu-Feng Wang, Bo Tian, Li-Cai Liu, Min Li & Bo Qin

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  1. Yu-Feng Wang
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  2. Bo Tian
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  3. Li-Cai Liu
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  4. Min Li
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  5. Bo Qin
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Correspondence to Bo Tian.

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Wang, YF., Tian, B., Liu, LC. et al. N-soliton solutions and asymptotic analysis for a Kadomtsev–Petviashvili–Schrödinger system for water waves. Z. Angew. Math. Phys. 66, 2543–2553 (2015). https://doi.org/10.1007/s00033-015-0538-6

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  • DOI: https://doi.org/10.1007/s00033-015-0538-6

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