2014/11/14 by Xiaorui Hu, Yuqi Li, Hu, Xiaorui +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Group Theory (math.GR) #Nonlinear Waves and Solitons #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1411.3798
openalex publication_date 2014/11/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
To search for inequivalent group invariant solutions, a general and systematic approach is established to construct two-dimensional optimal systems, which is based on commutator relations, adjoint matrix and the invariants. The details of computing all the invariants for two-dimensional subalgebras is presented and the optimality of twodimensional optimal systems is shown clearly under different values of invariants, with no further proof. Applying the algorithm to (1+1)-dimensional heat equation and (2+1)-dimensional Navier-Stokes (NS) equation, their twodimensional optimal systems are obtained, respectively. For the heat equation, eleven two-parameter elements in the optimal system are found one by one, which are discovered more comprehensive. The two-dimensional optimal system of NS equations is used to generate intrinsically different reduced ordinary differential equations and some interesting explicit solutions are provided.