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Kink-antikink scattering in the $\phi^4$ model is investigated in the limitwhen the static inter-soliton force vanishes. We observe the formation ofspectral walls and, further, identify a new phenomenon, the vacuum wall, whoseexistence gives rise to a bouncing structure for the annihilating solitons.Furthermore, we discover higher order spectral walls, i.e., spectral wallswhich form when higher harmonics enter the continuous spectrum. These higherorder spectral walls not only deform the soliton trajectories, they also can beobserved easily as very intense radiation bursts.

Kink-antikink scattering in the $\phi^4$ model without static intersoliton forces