The higher order rogue wave solutions of the Gerdjikov–Ivanov equation

2013/04/09 by Lijuan Guo, Yongshuai Zhang, Shuwei Xu +3 · 109 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Order (exchange) #Physics #Quantum mechanics #Rogue wave #Soliton #Term (time) #nlin.SI

paper · pdf · doi:10.1088/0031-8949/89/03/035501

published in Physica Scripta 89(3), 035501 (IOP Publishing)

arxiv created 2013/04/09 · openalex publication_date 2014/02/06 · arxiv updated 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We construct higher order rogue wave solutions for the Gerdjikov-Ivanov equation explicitly in term of determinant expression. Dynamics of both soliton and non-soliton solutions is discussed. A family of solutions with distinct structures are presented, which are new to the Gerdjikov-Ivanov equation.

Citations

• Modulation instability: The beginning

Cited by

• Rogue wave statistics and integrable turbulence in the Gerdjikov-Ivanov equation
• Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

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