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The reflection of active waves in a reaction-diffusion equation with spatial inhomogeneity is analyzed by use of the eikonal equation. The counterpart of the Rankine-Hugoniot relation, i.e. the shock condition, is derived for the transition layer in reaction-diffusion systems. In the case that the curvature effect of a wavefront is negligible, we show that the time evolution of a front is well described...
The scattering of nonlinear Schrodinger solitons due to an impurity in anharmonic lattices is studied numerically. At most one soliton is generated in both reflected and transmitted waves. Their amplitudes coincide very well with those of the theoretical result, which has been obtained through the inverse scattering method.
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