In this paper, a procedure for constructing discrete models of the high dimensional nonlinear evolution equanons is presented. In order to construct the difference model, with the aid of the potential system of the or...In this paper, a procedure for constructing discrete models of the high dimensional nonlinear evolution equanons is presented. In order to construct the difference model, with the aid of the potential system of the original equation and compatibility condition, the difference equations which preserve all Lie point symmetries can be obtained. As an example, invariant difference models of the （2＋1）-dimensional Burgers equation are presented.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11075055 and 11275072)the Innovative Research Team Program of the National Natural Science Foundation of China (Grant No. 61021004)+3 种基金National High Technology Research and Development Program of China (Grant No. 2011AA010101)the Leading Academic Discipline Project of Shanghai (Grant No. B412)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120076110024)the Shanghai Knowledge Service Platform Project (Grant No. ZF1213)
文摘In this paper, a procedure for constructing discrete models of the high dimensional nonlinear evolution equanons is presented. In order to construct the difference model, with the aid of the potential system of the original equation and compatibility condition, the difference equations which preserve all Lie point symmetries can be obtained. As an example, invariant difference models of the （2＋1）-dimensional Burgers equation are presented.
