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Riemann-Hilbert problem, integrability and reductions

  • * Corresponding author: R. I. Ivanov

    * Corresponding author: R. I. Ivanov 
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  • The present paper is dedicated to integrable models with Mikhailov reduction groups $G_R \simeq \mathbb{D}_h.$ Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the $G_R$-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with $\mathbb{D}_h$ symmetries are presented.

    Mathematics Subject Classification: Primary: 35K10, 35Q15; Secondary: 37K15, 35Q55.


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  • Figure 1.  Contour of a RHP with $ \mathbb{Z}_3 $ symmetry

    Figure 2.  Contour of the RHP $ \mathbb{D}_3 $ symmetry

    Figure 3.  Contour of the RHP for $ \mathbb{D}_2 $ symmetry (upper panel) and for $ \mathbb{D}_4 $ symmetry (lower panel)

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