학술논문
Potential systems of a Buckley–Leverett equation: Lie point symmetries and conservation laws.
Document Type
Article
Source
Subject
*CONSERVATION laws (Mathematics)
*CONSERVATION laws (Physics)
*TWO-phase flow
*ELLIPTIC functions
*EQUATIONS
*POROUS materials
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Language
ISSN
0259-9791
Abstract
In this work, we study a Buckley–Leverett equation of two-phase flow in porous media from the point of view of the Lie theory. We find that for some functions the equation has abundant exact solutions expressible in terms of Jacobi elliptic functions and consequently has many solutions in the form of periodic waves or solitary waves. We determine low-order conservation laws by using the multiplier method. From conservations laws, we construct the potential systems. From these systems we deduce potential equations. We study these equations from the point of view of Lie theory. Moreover, for these equations some nontrivial conservation laws are constructed by using the multipliers method. [ABSTRACT FROM AUTHOR]