SPECTRAL STABILITY OF ELLIPTIC SOLUTIONS TO THE DEFOCUSING LAKSHMANAN-PORSEZIAN-DANIEL EQUATION

Aiyong Chen; Yujing Chen; Haijun Hu

doi:10.11948/20250211

2026 Volume 16 Issue 2

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Aiyong Chen, Yujing Chen, Haijun Hu. SPECTRAL STABILITY OF ELLIPTIC SOLUTIONS TO THE DEFOCUSING LAKSHMANAN-PORSEZIAN-DANIEL EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 1074-1094. doi: 10.11948/20250211

Citation:

Aiyong Chen, Yujing Chen, Haijun Hu. SPECTRAL STABILITY OF ELLIPTIC SOLUTIONS TO THE DEFOCUSING LAKSHMANAN-PORSEZIAN-DANIEL EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 1074-1094. doi: 10.11948/20250211

SPECTRAL STABILITY OF ELLIPTIC SOLUTIONS TO THE DEFOCUSING LAKSHMANAN-PORSEZIAN-DANIEL EQUATION

1.
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China
2.
School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China
3.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, China

Author Bio: Email: 23110011921@stu.csust.edu.cn(Y. Chen); Email: huhaijun2000@163.com(H. Hu)
Corresponding author: Email: aiyongchen@163.com(A. Chen)
Fund Project: The authors were supported by the National Natural Science Foundation of China (No. 12571172), the Hunan Provincial Natural Science Foundation (No. 2023JJ30006), the Scientific Research Fund of Hunan Provincial Education Department of China (No. 21A0192) and the Postgraduate Scientific Research Innovation Project of Hunan Province (CX20251384)

Abstract

Abstract

In this paper, by exploiting the integrability of the defocusing Lakshmanan-Porsezian-Daniel (LPD) equation, we establish the spectral stability for the elliptic solutions with respect to subharmonic perturbations. We achieve this goal by constructing explicitly the squared-eigenfunction connection between the linear stability problem and its Lax pair. Furthermore, based on the spectral stability results, the linear stability for subharmonic perturbations is obtained by applying directly the Skew-symmetric Composed with Self-adjoint (SCS) basis lemma. Although it is challenging to determine analytically the spectra for all operators except the simplest ones, this research provides a detailed analytical description of the stable Lax spectrum and the stability spectrum.
- Spectral stability /
- LPD equation /
- elliptic solutions /
- subharmonic perturbations /
- integrability
MSC: 37K45, 35Q51, 33E05

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References

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