Modulation instability, higher-order rogue waves and dynamics of the Gerdjikov-Ivanov equation

DOI10.1016/j.wavemoti.2021.102795OpenAlexW3178033404MaRDI QIDQ2247573

Yi Zhang, Yu Lou, Rusuo Ye, Miao Li

Publication date: 17 November 2021

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.wavemoti.2021.102795

zbMATH Keywords

Darboux transformationmodulation instabilityGerdjikov-Ivanov equationhigher-order rogue wavesvariable separation technique

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Partial differential equations (35-XX)

Related Items

Breathers on elliptic function background for a generalized nonlinear Schrödinger equation with higher-order terms ⋮ Higher-order semi-rational solutions for the coupled complex modified Korteweg-de Vries equation ⋮ Binary Darboux transformation for the Gerdjikov-Ivanov equation ⋮ Interactional solutions of the extended nonlinear Schrödinger equation with higher-order operators ⋮ Rogue waves, modulation instability of the \((2+1)\)-dimensional complex modified Korteweg-de Vries equation on the periodic background ⋮ \(N\)-soliton asymptotic analysis on the Gerdjikov-Ivanov equation for the Alfvén waves in a plasma ⋮ Rogue waves as modulational instability result in one-dimensional nonlinear triatomic acoustic metamaterials

Cites Work

• Unnamed Item
• Unnamed Item
• Solitons, breathers and rogue waves for the coupled Fokas-Lenells system via Darboux transformation
• Vector rational and semi-rational rogue wave solutions in the coupled complex modified Korteweg-de Vries equations
• Exact solution to higher-order nonlinear equations through gauge transformation
• Variable separation and algebro-geometric solutions of the Gerdjikov-Ivanov equation
• A Riemann-Hilbert approach to the Chen-Lee-Liu equation on the half line
• Solitons and dynamics for the integrable nonlocal pair-transition-coupled nonlinear Schrödinger equation
• Exact solutions of nonlocal Fokas-Lenells equation
• Integrable evolution systems based on Gerdjikov–Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation
• A family of completely integrable multi-Hamiltonian systems explicitly related to some celebrated equations
• The rogue wave and breather solution of the Gerdjikov-Ivanov equation
• Water waves, nonlinear Schrödinger equations and their solutions
• An exact solution for a derivative nonlinear Schrödinger equation
• Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
• Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation
• Gauge transformations of constrained KP flows: New integrable hierarchies
• Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations
• Riemann-Hilbert method and N-soliton for two-component Gerdjikov-Ivanov equation
• General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation
• Oceanic Rogue Waves