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Long-Time Asymptotics of a Three-Component Coupled mKdV System

Author

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  • Wen-Xiu Ma

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
    Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA
    College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China)

Abstract

We present an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a 4 × 4 matrix spectral problem. An integrable coupled mKdV hierarchy with three potentials is first generated. Based on the corresponding oscillatory Riemann-Hilbert problem, the leading asympototics of the three-component mKdV system is then evaluated by using the nonlinear steepest descent method.

Suggested Citation

  • Wen-Xiu Ma, 2019. "Long-Time Asymptotics of a Three-Component Coupled mKdV System," Mathematics, MDPI, vol. 7(7), pages 1-38, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:573-:d:243546
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    References listed on IDEAS

    as
    1. Wen-Xiu Ma & Jie Li & Chaudry Masood Khalique, 2018. "A Study on Lump Solutions to a Generalized Hirota-Satsuma-Ito Equation in (2+1)-Dimensions," Complexity, Hindawi, vol. 2018, pages 1-7, December.
    2. Ma, W.X., 1995. "Symmetry constraint of MKdV equations by binary nonlinearization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 467-481.
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