EXACT SOLUTIONS OF TWO HIGH ORDER DERIVATIVE NONLINEAR SCHRÖDINGER EQUATIONS: DYNAMICAL SYSTEM METHOD

Zhilong Shi; Linru Nie; Jibin Li

doi:10.11948/20240451

2025 Volume 15 Issue 3

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Zhilong Shi, Linru Nie, Jibin Li. EXACT SOLUTIONS OF TWO HIGH ORDER DERIVATIVE NONLINEAR SCHRÖDINGER EQUATIONS: DYNAMICAL SYSTEM METHOD[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1820-1829. doi: 10.11948/20240451

Citation:

Zhilong Shi, Linru Nie, Jibin Li. EXACT SOLUTIONS OF TWO HIGH ORDER DERIVATIVE NONLINEAR SCHRÖDINGER EQUATIONS: DYNAMICAL SYSTEM METHOD[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1820-1829. doi: 10.11948/20240451

EXACT SOLUTIONS OF TWO HIGH ORDER DERIVATIVE NONLINEAR SCHRÖDINGER EQUATIONS: DYNAMICAL SYSTEM METHOD

1.
Faculty of Architectural Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650500, China
2.
Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan 650500, China
3.
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China

Author Bio: Email: linrunie@126.com(L. Nie); Email: lijb@zjnu.cn(J. Li)
Corresponding author: Email: dragon24011@163.com(Z. Shi)
Fund Project: The authors were supported by National Natural Science Foundation of China (11871231, 12071162, 11701191) and National Science Foundation of Fujian Province (2021J01303)

Abstract

Abstract

For two generalization models of the first type derivative nonlinear Schrödinger (DNLSI) equation and the second type derivative nonlinear Schrödinger (DNLSII) equation, by using the method of dynamical systems to investigate the existence of exact explicit solutions with the form $ q(x,t)=\phi(\xi)\exp{[i(\kappa x-\omega t+\theta(\xi))]}, \xi=x-ct. $ This paper show that in some given parameter conditions, explicit exact parametric representations of $ \phi(\xi)$ and $\theta(\xi) $ can be given.
- Bifurcation /
- exact solution /
- planar integrable system /
- generalization models of Kaup-Newell equation and Chen-Lee-Liu equation
MSC: 34C23, 35Q51-53, 58J55

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References

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