再论弹性大挠度问题von Kármán方程与量子本征值问题Schrǒdinger方程的关系

本文是文1]的继续和改善。利用本文的结果,还可以改善文2～3]中有关弹性大挠度问题的讨论。在本文中,我们再次对弹性大挠度问题的von Kármán方程进行简化,使它最终成为非线性Schr?dinger方程。其次,在本文中我们对AKNS方程在多维条件下进行了更为对称的拓展。由于非线性Schr?dinger方程与AKNS方程即Dirac方程的可积性条件相联系,因此,弹性大挠度问题可以用逆散射方法求得其精确解,也就是说,它完全成了量子本征值问题。对于正交各向异性大挠度问题,本文也作了推论。

Further Study of the Relation of von Karman Equation for Elastic Large Deflection Problem and Schrodinger Equation for Quantum Eigenvalues Problem

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 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.