Abstract
As effective tools that can be used to solve both continuous and discrete dynamic systems, symmetry analysis, conserved quantities and Ba ¨cklund transformations of dynamic systems on time-space scales are studied, which unify and generalize the continuous and discrete cases. Applying the method to heat equation and Burgers equation, we get symmetries, group invariant solutions and Ba ¨cklund transformations of the system on time-space scales. The results are applied to approximately simulate motion process of traffic flow with given initial condition. The study of nonlinear systems on time-space scales provides a theoretical basis for revealing the internal physical mechanism of the systems. Applications of the method to other dynamic equations on time-space scales deserve to be further studied.
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