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In this work, we study the asymptotic characteristics of high‐order solitons for the focusing Kundu–Eckhaus (KE) equation. Based on the loop group theory, we construct the general Darboux transformation within the framework of Riemann–Hilbert problems to derive the general high‐order soliton solution. Using high‐order Bäcklund transformation, we derive the leading order term of the determinant solution to obtain the asymptotic representation for the high‐order soliton solution. Furthermore, this method is also extended to the construction of more general high‐order cases with multiple poles. We further find that if a soliton propagates along the logarithm characteristic curve, the high‐order soliton can be decomposed into n$$ n $$ individual solitons with the same amplitude and velocity. Finally, these solutions are theoretically and graphically analyzed in detail. [ABSTRACT FROM AUTHOR]

In this paper, the inverse scattering transform of a two-component modified Korteweg–de Vries equation is under investigation, which is one of the important nonlinear models in mathematics and physics. The spectral analysis with a 4 × 4 Lax pair is performed for the two-component modified Korteweg–de Vries equation, from which a Riemann Hilbert problem is strictly formulated. Moreover, multi-soliton solutions to the two-component modified Korteweg–de Vries equation are obtained through a particular Riemann–Hilbert formulation. Finally, some figures are presented to reveal the soliton features of the two-component modified Korteweg–de Vries equation. [ABSTRACT FROM AUTHOR]