Schrödinger equations on elliptic curves: symmetries, solutions and eigenvalue problem

被引：0

作者：

Valentin Lychagin

Mikhail Roop

机构：

[1] Russian Academy of Sciences,V.A. Trapeznikov Institute of Control Sciences

来源：

Analysis and Mathematical Physics | 2020年 / 10卷

关键词：

Schrödinger type equations; Symmetries; Integrable potentials; Lamé equation; Eigenvalue problem; 34A26; 34A05; 34B09;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we study Schrödinger equations on elliptic curves called generalized Lamé equations. We suggest a method of finding integrable potentials for Schrödinger type equations. We apply this method to the Lamé equations and provide a sequence of integrable potentials for which the eigenvalue problem is solved explicitly.

引用

共 8 条

[1]

Lamé G(1837)Sur les surfaces isothermes dans les corps homogenes en équilibre de température J. Math. Pures Appl. 2 147-188

[2]

Liang Jiu-Qing(1992)Solitons, bounces and sphalerons on a circle Phys. Lett. B 282 105-110

[3]

Müller-Kirsten HJW(2005)Integrability of Hamiltonian systems and the Lamé equation Appl. Math. Lett. 18 555-561

[4]

Tchrakian DH(1981)On algebraic solutions of Lamé’s differential equation J. Differ. Equ. 41 44-58

[5]

Kasperczuk SP(2007)Finite dimensional dynamics for evolutionary equations Nonlinear Dyn. 48 29-48

[6]

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