FURTHER STUDY OF THE RELATION OF VON KÁRMÁN EQUATION FOR ELASTIC LARGE DEFLECTION PROBLEM AND SCHRÖDINGER EQUATION FOR QUANTUM EIGENVALUES PROBLEM

Abstract

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 thispaper. We again simplify the von Karman equation for elastic large deflection problem, and finally turn it into the nonlinear Schrodinger equation in this paper. Secondly, we expand the AKNS equation to still more symmetrical degree under many dimensional conditions in thispaper. Owing to connection between the nonlinear Schrodinger equation and the integrability condition for the AKNS equation or the Dirac equation, we can obtain the exact solution/or 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.

Key words: system of generalized mixed equilibrium problem, auxiliary principle, iterative algorithm, reflexive Banach space

Shen Hui-chuan . FURTHER STUDY OF THE RELATION OF VON KÁRMÁN EQUATION FOR ELASTIC LARGE DEFLECTION PROBLEM AND SCHRÖDINGER EQUATION FOR QUANTUM EIGENVALUES PROBLEM. Applied Mathematics and Mechanics (English Edition), 1987, 8(6): 561-568.

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References

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