Abstract
In this paper, a new theory of constructing nonlinear Galerkin optimal truncated Low-Dimensional Dynamical Systems (LDDSs) directly from partial differential equations has been developed. Applying the new theory to the nonlinear Burgers' equation, it is shown that a nearly perfect LDDS can be gotten, and the initial-boundary conditions are automatically included in the optimal bases. The nonlinear Galerkin method does not, have advantages within the optimization process, but it can significantly improve the results, after the Galerkin optimal bases have been gotten.
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