10 citations · 29 across the 20 of their papers we have counts for
5 papers · 1 filter
Tree Diagram Lie Algebras of Differential Operators and Evolution Partial Differential Equations
Xiaoping Xu
A tree diagram is a tree with positive integral weight on each edge, which is a notion generalized from the Dynkin diagrams of finite-dimensional simple Lie algebras. We introduce…
Flag Partial Differential Equations and Representations of Lie Algebras
Xiaoping Xu
In this paper, we solve the initial value problems of variable-coefficient generalized wave equations associated with trees and a large family of linear constant-coefficient partia…
Stable-Range Approach to the Equation of Nonstationary Transonic Gas Flows
Xiaoping Xu
Using certain finite-dimensional stable range of the nonlinear terms, we obtain large families of exact solutions parameterized by functions for the equation of nonstationary trans…
New Algebraic Approaches to Classical Boundary Layer Problems
Xiaoping Xu
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for…
Asymmetric and Moving-Frame Approaches to Navier-Stokes Equations
Xiaoping Xu
In this paper, we introduce a method of imposing asymmetric conditions on the velocity vector with respect to independent variables and a method of moving frame for solving the thr…