THE BÄCKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF SOLUTIONS FOR THE LIOUVILLE’S EQUATION IN HIGHER DIMENSIONS

Applied Mathematics and Mechanics (English Edition) ›› 1984, Vol. 5 ›› Issue (6): 1777-1782.

THE BÄCKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF SOLUTIONS FOR THE LIOUVILLE’S EQUATION IN HIGHER DIMENSIONS

黄迅成

Shanghai Institute of Computing Technique, Shanghai

收稿日期:1983-04-20 出版日期:1984-11-18 发布日期:1984-11-18

THE BÄCKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF SOLUTIONS FOR THE LIOUVILLE’S EQUATION IN HIGHER DIMENSIONS

Huang Xun-cheng

Shanghai Institute of Computing Technique, Shanghai

Received:1983-04-20 Online:1984-11-18 Published:1984-11-18

摘要/Abstract

摘要： In this paper, we show that Backlund transformation derived by Leibbrandt et al. for the Liouville’s equation in three spatial dimensions, ▽²a=expa, ▽²=-∂_x²+∂_y²+∂_z² can be decomposed into several Backlund transformations for the same equation in two spatial dimensions, moreover, the superposition formula which is derived from this transformation is actually invalid, thus the discussions based on that formula is incorrect as well. We also considered some results about the Liouville’s equation in N spatial dimensions.

关键词: engineering structure, dynamic response, dynamic sensitivity, reliability constraint, optimal design

Abstract: In this paper, we show that Backlund transformation derived by Leibbrandt et al. for the Liouville’s equation in three spatial dimensions, ▽²a=expa, ▽²=-∂_x²+∂_y²+∂_z² can be decomposed into several Backlund transformations for the same equation in two spatial dimensions, moreover, the superposition formula which is derived from this transformation is actually invalid, thus the discussions based on that formula is incorrect as well. We also considered some results about the Liouville’s equation in N spatial dimensions.

Key words: engineering structure, dynamic response, dynamic sensitivity, reliability constraint, optimal design

黄迅成. THE BÄCKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF SOLUTIONS FOR THE LIOUVILLE’S EQUATION IN HIGHER DIMENSIONS[J]. Applied Mathematics and Mechanics (English Edition), 1984, 5(6): 1777-1782.

Huang Xun-cheng. THE BÄCKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF SOLUTIONS FOR THE LIOUVILLE’S EQUATION IN HIGHER DIMENSIONS[J]. Applied Mathematics and Mechanics (English Edition), 1984, 5(6): 1777-1782.

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THE BÄCKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF SOLUTIONS FOR THE LIOUVILLE’S EQUATION IN HIGHER DIMENSIONS

THE BÄCKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF SOLUTIONS FOR THE LIOUVILLE’S EQUATION IN HIGHER DIMENSIONS

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