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Further study of the relation of von Kármán equation for elastic large deflection problem and Schrödinger equation for quantum eigenvalues problem

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Abstract

This work is the continuation and improvement of the discussion of Ref. [1]. We also improve the discussion of Refs. [2–3] on the elastic large deflection problem by results of this paper. We again simplify the von Kármán equation for elastic large deflection problem, and finally turn it into the nonlinear Schrödinger equation in this paper. Secondly, we expand the AKNS equation to still more symmetrical degree under many dimensional conditions in this paper. Owing to connection between the nonlinear Schrödinger equation and the integrability condition for the AKNS equation or the Dirac equation, we can obtain the exact solution for elastic large deflection problem by inverse scattering method. In other words, the elastic large deflection problem wholly becomes a quantum eigenvalues problem.

The large deflection problem with orthorhombic anisotropy is also deduced in this paper.

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  1. Fundamental Physics Centre, University of Science and Technology of China, Hefei

    Shen Hui-chuan

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  1. Shen Hui-chuan
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Communicated by Chien Wei-zang

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Hui-chuan, S. Further study of the relation of von Kármán equation for elastic large deflection problem and Schrödinger equation for quantum eigenvalues problem. Appl Math Mech 8, 561–568 (1987). https://doi.org/10.1007/BF02017405

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  • DOI: https://doi.org/10.1007/BF02017405

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