Multi-soliton solutions for the three types of nonlocal Hirota equations via Riemann–Hilbert approach

doi:10.1088/1572-9494/ac8afc

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Communications in Theoretical Physics ›› 2022, Vol. 74 ›› Issue (11): 115004. doi: 10.1088/1572-9494/ac8afc

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Multi-soliton solutions for the three types of nonlocal Hirota equations via Riemann–Hilbert approach

Yindong Zhuang, Yi Zhang^,^∗(), Heyan Zhang, Pei Xia

Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received: 2022-05-27 Revised: 2022-08-03 Accepted: 2022-08-19 Published: 2022-10-28
Contact: Yi Zhang E-mail:zy2836@163.com
About author: First author contact:∗Author to whom any correspondence should be addressed.

Abstract

Abstract:

The purpose of the paper is to formulate multi-soliton solutions for the nonlocal Hirota equations via the Riemann–Hilbert (RH) approach. The RH problems are constructed and the zero structures are studied via performing spectral analysis of the Lax pair. Then we consider three types of nonlocal Hirota equations by discussing different symmetry reductions of the potential matrix. On the basis of the resulting matrix RH problem under the restriction of the reflectionless case, we successfully obtain the multi-soliton solutions of the nonlocal Hirota equations.

Key words: the nonlocal Hirota equation, Riemann–Hilbert approach, multi-soliton solutions

Yindong Zhuang, Yi Zhang, Heyan Zhang, Pei Xia, Commun. Theor. Phys. 74 (2022) 115004.

Figures/Tables 3

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Multi-soliton solutions for the three types of nonlocal Hirota equations via Riemann–Hilbert approach

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