Keywords
N-solutions
Variable coefficient nonlocal Gerdjikov-Ivanov (GI) equation
Spectral analysis
Submitted : 2024-12-07
Accepted : 2024-12-22
Published : 2025-01-06
Abstract
This paper adopts the Riemann-Hilbert method to investigate a variable coefficient nonlocal Gerdjikov-Ivanov (GI) equation. A solvable regular Riemann-Hilbert problem with simple zeros is constructed through spectral analysis. Furthermore, the paper provides the determinant form of N-solutions for the equation.
References
Wen L, Fan E, 2022, N-Soliton Solution of The Kundu-Type Equation Via Riemann-Hilbert Approach. Acta Mathematica Scientia, 2022(40): 113–126.
Wang D, Wang X, 2018, Long-time Asymptotics and the Bright N-soliton Solutions of the Kundu–Eckhaus Equation via the Riemann-Hilbert Approach. Nonlinear Analysis: Real World Applications, 2018(41): 334–361.
Liu W, Geng X, 2023, Spectral Analysis and Long-time Asymptotics for the Harry Dym-type Equation with the Schwartz Initial Data. Journal of Differential Equations, 2023(357): 181–235.
Geng X, Wang K, 2021, Long-time Asymptotics for the Spin-1 Gross–Pitaevskii Equation. Communications in Mathematical Physics, 2021(382): 585–611.
Takasaki K, 2005, Tyurin Parameters of Commuting Pairs and Infinite Dimensional Grassmann Manifold. Rokko Lectures in Mathematics, 2005(18): 289–304.
Hedenmalm H, Wennman A, 2024, Riemann-Hilbert Hierarchies for Hard Edge Planar Orthogonal Polynomials. American Journal of Mathematics, 146(2): 371–403.
Gerdjikov V, Ivanov I, 1983, A Quadratic Pencil of General Type and Nonlinear Evolution Equations II. Hierarchies of Hamiltonian Structures. Bulgarian Journal of Physics, 1983(10): 130–143.
Li M, Zhang Y, 2021, Exact Solutions of the nonlocal Gerdjikov-Ivanov Equation. Communications in Theoretical Physics, 73(10): 105005.