Algebro-geometric solutions for the Gerdjikov-Ivanov hierarchy

DOI10.1063/1.4812559zbMath1287.35081arXiv1207.0574OpenAlexW2012731439MaRDI QIDQ5407610

Yu Hou, Peng Zhao, En-gui Fan

Publication date: 7 April 2014

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

Full work available at URL: https://arxiv.org/abs/1207.0574

zbMATH Keywords

Chen-Lee-Liu equationBaker-Akhiezer functionsDubrovin-type equationsGerdjikov-Ivanov equationKaup-Newell equationderivate nonlinear Schrödinger equationsGerdjikov-Ivanov hierarchy

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) Meromorphic functions of several complex variables (32A20) Soliton solutions (35C08)

Related Items

The algebro-geometric solutions for the Fokas-Olver-Rosenau-Qiao (FORQ) hierarchy ⋮ The complex Hamiltonian system in the Gerdjikov-Ivanov equation and its applications ⋮ Higher-order algebraic soliton solutions of the Gerdjikov-Ivanov equation: asymptotic analysis and emergence of rogue waves ⋮ The long-time asymptotics of the derivative nonlinear Schrödinger equation with step-like initial value ⋮ Initial-Boundary Value Problem for Two-Component Gerdjikov–Ivanov Equation with 3 × 3 Lax Pair on Half-Line ⋮ Inverse scattering transform for the Gerdjikov-Ivanov equation with nonzero boundary conditions ⋮ Finite gap integration of the derivative nonlinear Schrödinger equation: a Riemann-Hilbert method ⋮ Dbar-dressing method for the Gerdjikov-Ivanov equation with nonzero boundary conditions ⋮ \( \overline{\partial} \)-dressing method for the coupled Gerdjikov-Ivanov equation ⋮ A two-component generalization of Burgers' equation with quasi-periodic solution ⋮ On quasiperiodic solutions of the modified Kadomtsev-Petviashvili hierarchy ⋮ Trace formula and new form of \(N\)-soliton to the Gerdjikov-Ivanov equation ⋮ Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov-Ivanov equation under the zero/nonzero background ⋮ Conservation laws and \(\tau\)-symmetry algebra of the Gerdjikov-Ivanov soliton hierarchy ⋮ Initial-boundary value problem for the two-component Gerdjikov-Ivanov equation on the interval ⋮ Riemann-Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary conditions

Cites Work

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• Algebro-geometric solutions for the Hunter-Saxton hierarchy
• New factorization of the Kaup-Newell hierarchy
• Algebro-geometric solutions of the Camassa-Holm hierarchy
• Variable separation and algebro-geometric solutions of the Gerdjikov-Ivanov equation
• Uniformly constructing finite-band solutions for a family of derivative nonlinear Schrödinger equations
• On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KdV poten\-tials
• Algebro-geometric solutions of the Baxter-Szegő difference equation
• Integrable evolution systems based on Gerdjikov–Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation
• Multi-Soliton Solutions of a Derivative Nonlinear Schrödinger Equation
• Painleve analysis of the non-linear Schrodinger family of equations
• Exact solutions of the multidimensional derivative nonlinear Schrodinger equation for many-body systems of criticality
• Periodic solutions of the KdV equation
• A complete solution of the periodic Toda problem
• On the modulation of water waves in the neighbourhood of kh ≈ 1.363
• An exact solution for a derivative nonlinear Schrödinger equation
• An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy
• The finite-band solution of the Jaulent–Miodek equation
• GENERALIZED r-MATRIX STRUCTURE AND ALGEBRO-GEOMETRIC SOLUTION FOR INTEGRABLE SYSTEM
• Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
• ALGEBRO-GEOMETRIC SOLUTIONS OF THE BOUSSINESQ HIERARCHY
• Finite-band solutions of the classical Boussinesq–Burgers equations
• Algebro-geometric solution of the 2+1 dimensional Burgers equation with a discrete variable
• Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation

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