Quasi-Periodic Solutions to the Nonlocal Nonlinear Schrödinger Equations

Liang Guan ^[1] ; Xianguo Geng ^[2] ; Xue Geng ^[1]
1. [1] Anyang Normal University
  
  Anyang Normal University
  
  China
2. [2] Zhengzhou University
  
  Zhengzhou University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
Idioma: inglés
Enlaces
- Texto completo
Resumen
- A hierarchy of nonlocal nonlinear Schrödinger equations is derived by using the Lenard gradients and the zero-curvature equation. According to the Lax matrix of the nonlocal nonlinear Schrödinger equations, we introduce a hyperelliptic Riemann surface Kn of genus n, from which Dubrovin-type equations, meromorphic function, and Baker– Akhiezer function are established. By the theory of algebraic curves, the corresponding flows are straightened by resorting to the Abel–Jacobi coordinates. Finally, we obtain the explicit Riemann theta function representations of the Baker–Akhiezer function, specifically, that of solutions for the hierarchy of nonlocal nonlinear Schrödinger equations in regard to the asymptotic properties of the Baker–Akhiezer function.