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arXiv · 1411.3798

The construction of two-dimensional optimal systems for the invariant solutions

Xiaorui Hu·Yuqi Li·Yong Chen
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Abstract

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.

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Xiaorui Hu, Yuqi Li, Yong Chen. 2014-11-14. The construction of two-dimensional optimal systems for the invariant solutions. https://arxiv.org/abs/1411.3798

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