Abstract
We propose the group-theoretical approach which enables one to generate solutions of equations of mathematical physics in nonhomogeneous media from solutions of the same problem in a homogeneous medium. The efficiency of this method is illustrated with examples of thermal neutron diffusion problems. Such problems appear in neutron physics and nuclear geophysics. The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.
Highlights
The group-theoretical analysis is known to be used for the construction of exact solutions of a number of linear and nonlinear equations of mathematical physics [1, 2]
In this paper we use the group of transformations to solve the direct problem, namely, the problem of stationary diffusion of neutrons in a nonhomogeneous medium for the linear and point source in two- and three-dimensional space
By virtue of the group method, we can construct the solution of neutron diffusion equation in nonhomogeneous medium where both coefficients D and Σ are not constant but variable functions on r
Summary
The group-theoretical analysis is known to be used for the construction of exact solutions of a number of linear and nonlinear equations of mathematical physics [1, 2]. In this paper we use the group of transformations to solve the direct problem, namely, the problem of stationary diffusion of neutrons in a nonhomogeneous medium for the linear and point source in two- and three-dimensional space. By virtue of the group method, we can construct the solution of neutron diffusion equation in nonhomogeneous medium where both coefficients D and Σ are not constant but variable functions on r. Such a model extends to more adequately describe the properties of the nonhomogeneous medium. By analogy with the previous example, making use of the conformal transformations, we can construct solutions of diffusion equations in the three-dimensional space (for a point source) for a nonhomogeneous medium.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
