Application of the Riemann–Hilbert method to the vector modified Korteweg-de Vries equation

  • Xiu-Bin WangEmail author
  • Bo Han
Original paper


Under investigation in this paper is the inverse scattering transform of the vector modified Korteweg-de Vries (vmKdV) equation, which can be reduced to several integrable systems. For the direct scattering problem, the spectral analysis is performed for the equation, from which a Riemann–Hilbert problem is well constructed. For the inverse scattering problem, the Riemann–Hilbert problem corresponding to the reflection-less case is solved. Furthermore, as applications, three types of multi-soliton solutions are found. Finally, some figures are presented to discuss the soliton behaviors of the vmKdV equation.


Inverse scattering transform Riemann–Hilbert problem Multi-soliton solutions 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinPeople’s Republic of China

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