关于非线性广义阿贝尔积分方程的解

B. Kalimbetov
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引用次数: 0

摘要

众所周知,电子学、核物理学、光学和天体物理学等许多问题都是用第一类阿贝尔积分方程来描述的。本文研究了一类非线性广义阿贝尔方程,并证明了它的解可以表示为幂函数的积分。结果表明,构造的解析解与利用计算机数学系统Maple得到的符号解重合,并给出了它们的平面图和空间图。
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About Solution of the Nonlinear Generalized Abel Integral Equation
As is known, many problems of electronics, nuclear physics, optics and astrophysics, etc. are described by the Abel integral equation of the first kind. In this paper we consider the nonlinear generalized Abel equation and show that its solution can be represented as an integral of a power function. It is shown that the constructed analytical solution and the symbolic solution obtained by means of the computer mathematics system Maple coincides, and their planar and spatial graphs are presented.
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