The integrable system related to a nonself-adjoint fourth-order eigenvalue problem and involutive solution

Hongjuan Fu; Xu Han; Jiao Li

doi:10.1117/12.3036679

21 July 2024 The integrable system related to a nonself-adjoint fourth-order eigenvalue problem and involutive solution

Hongjuan Fu, Xu Han, Jiao Li

Proceedings Volume 13219, Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024); 132193D (2024) https://doi.org/10.1117/12.3036679
Event: 4th International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2024), 2024, Kaifeng, China

Abstract

Soliton theory and integrable system have important applications in the fields of mathematics and physics, and their research is of great significance to our understanding of nature, the search for new integrable systems has been the focus of integrable theory. Due to its complexity, little is known about the high-order and high-dimensional eigenvalue problems.In this paper, based on the nonlinear method of eigenvalue problem, we discuss a non-self-adjoint fourth-order eigenvalue problem, by using the relation between the potential function and the characteristic function, the Bargmann constrained system is obtained. Secondly, a set of suitable Jacobi-ostrograndsky coordinate systems is constructed, in which Lax pairs of the evolution equations corresponding to the fourth-order eigenvalue problem are nonlinear, the exact integrable Hamiltonian canonical systems on symplectic manifolds are obtained. Finally, the involution representation of the solutions of the corresponding evolution equations on the finite dimensional subspace is obtained. The solutions of the nonlinear evolution equations are constructed by using the solutions of the classical systems. The problem of high order and high dimension eigenvalue problem is solved.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

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Hongjuan Fu, Xu Han, and Jiao Li "The integrable system related to a nonself-adjoint fourth-order eigenvalue problem and involutive solution", Proc. SPIE 13219, Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024), 132193D (21 July 2024); https://doi.org/10.1117/12.3036679

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KEYWORDS

Complex systems

Solitons

Lutetium

Mathematics

Physics

Lithium

Matrices

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