Huang Xun-cheng. The Backlund Transformation and Nonlinear Superposition Formula of Solutions for the Liouville’s Equation in Higher Dimensions[J]. Applied Mathematics and Mechanics, 1984, 5(6): 801-807.
Citation:
Huang Xun-cheng. The Backlund Transformation and Nonlinear Superposition Formula of Solutions for the Liouville’s Equation in Higher Dimensions[J]. Applied Mathematics and Mechanics, 1984, 5(6): 801-807.
Huang Xun-cheng. The Backlund Transformation and Nonlinear Superposition Formula of Solutions for the Liouville’s Equation in Higher Dimensions[J]. Applied Mathematics and Mechanics, 1984, 5(6): 801-807.
Citation:
Huang Xun-cheng. The Backlund Transformation and Nonlinear Superposition Formula of Solutions for the Liouville’s Equation in Higher Dimensions[J]. Applied Mathematics and Mechanics, 1984, 5(6): 801-807.
In this paper, we show that Backlund transformation derived by Leibbraadt et al for the Liouvilles equation in three spatial dimeasions,∇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.
Solitons 82,Abstracts of Cpaference aced Workshop Talks and.Posters.Edinburgh,England,Aug,(1982).
[2]
Leibbrandt,G.,S,S,Wang and N,Zamani,Backlund generated solutions of Liouville's equdtion and their graphical representations in three spatial dimensioas,d.Math.Phys.,23,9(1982),1566-1572.
[3]
Leibbrandt,G.,Nonlinear superposition for Liouville's equation in three spatial dimensions,Left,Math,Phys.,4(1984).317-321.
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