Based on G-hulls and G-kernels under the meaning of G-methods on sets, we introduce the concepts of G-hull-closed sets, G-kernel-open sets, G-kernel-neighborhoods and G-kernel-derived sets, discuss some related proper...Based on G-hulls and G-kernels under the meaning of G-methods on sets, we introduce the concepts of G-hull-closed sets, G-kernel-open sets, G-kernel-neighborhoods and G-kernel-derived sets, discuss some related properties. In particular, we define pointwise G-methods, prove the consistency of G-closed sets and G-hull-closed sets, G-open sets and Gkernel-open sets, G-neighborhoods and G-kernel-neighborhoods, G-derived sets and G-kernelderived sets under this method, and enrich some results about G-closed sets, G-open sets,G-interiors, G-neighborhoods and G-derived sets in sets. At the same time, we put forward some problems for further research.展开更多
Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to t...Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations.The search for solutions of these systems by using the G'/G-method has yielded certain exact solutions expressed by rational functions,hyperbolic functions,and trigonometric functions.Some figures are given to show the properties of the solutions.展开更多
基金Supported by the Special Youth Project of Ningde Normal University(Grant No.2016Q34)the National Natural Science Foundation of China(Grant No.11471153)
文摘Based on G-hulls and G-kernels under the meaning of G-methods on sets, we introduce the concepts of G-hull-closed sets, G-kernel-open sets, G-kernel-neighborhoods and G-kernel-derived sets, discuss some related properties. In particular, we define pointwise G-methods, prove the consistency of G-closed sets and G-hull-closed sets, G-open sets and Gkernel-open sets, G-neighborhoods and G-kernel-neighborhoods, G-derived sets and G-kernelderived sets under this method, and enrich some results about G-closed sets, G-open sets,G-interiors, G-neighborhoods and G-derived sets in sets. At the same time, we put forward some problems for further research.
文摘Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations.The search for solutions of these systems by using the G'/G-method has yielded certain exact solutions expressed by rational functions,hyperbolic functions,and trigonometric functions.Some figures are given to show the properties of the solutions.
