Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations

DOI10.1080/14029251.2015.996438zbMath1420.35064arXiv1501.07634OpenAlexW3104010400MaRDI QIDQ5230972

Halis Yilmaz

Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.07634

zbMATH Keywords

derivative nonlinear Schrödinger equationDarboux transformationquasideterminantsGerdjikov-Ivanov equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)

Related Items (18)

Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields ⋮ The complex Hamiltonian system in the Gerdjikov-Ivanov equation and its applications ⋮ Binary Darboux transformation for the Gerdjikov-Ivanov equation ⋮ Darboux Transformation for the Hirota Equation ⋮ Higher-order algebraic soliton solutions of the Gerdjikov-Ivanov equation: asymptotic analysis and emergence of rogue waves ⋮ Traveling wave solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity ⋮ Exact solutions of the nonlocal Gerdjikov-Ivanov equation ⋮ On integrable wave interactions and Lax pairs on symmetric spaces ⋮ The long-time asymptotics of the derivative nonlinear Schrödinger equation with step-like initial value ⋮ An integrable generalization of the D-Kaup-Newell soliton hierarchy and its bi-Hamiltonian reduced hierarchy ⋮ Modulational instability and location controllable lump solutions with mixed interaction phenomena for the \((2+1)\)-dimensional Myrzakulov-Lakshmanan-IV equation ⋮ Optical soliton perturbation for Gerdjikov-Ivanov equation via two analytical techniques ⋮ Bifurcations and exact traveling wave solutions of Gerdjikov-Ivanov equation with perturbation terms ⋮ Soliton, breather and rogue wave solutions of the coupled Gerdjikov-Ivanov equation via Darboux transformation ⋮ \(N\)-soliton asymptotic analysis on the Gerdjikov-Ivanov equation for the Alfvén waves in a plasma ⋮ Quasi-Grammian solutions of the coupled Gerdjikov-Ivanov equation ⋮ Modulation instability, higher-order rogue waves and dynamics of the Gerdjikov-Ivanov equation ⋮ The initial-boundary value for the combined Schrödinger and Gerdjikov-Ivanov equation on the half-line via the Riemann-Hilbert approach

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