Search for long-living topological solutions of the nonlinear φ⁴ field theory

We look for long-living topological solutions of classical nonlinear (1+1)-dimensional φ4 field theory. To that effect we use the well-known cut-and-match method. In this framework, new long-living states are obtained in both topological sectors. In particular, in one case a highly excited state of a kink is found. We discover several ways of energy reset. In addition to the expected emission of wave packets (with small amplitude), for some selected initial conditions the production of kink-antikink pairs results in a large energy reset. Also, the topological number of a kink in the central region changes in the contrast of conserving full topological number. At lower excitation energies there is a long-living excited vibrational state of the kink; this phenomenon is the final stage of all considered initial states. Over time this excited state of the kink changes to a well-known linearized solution - a discrete kink excitation mode. This method yields a qualitatively new way to describe the large-amplitude bion, which was detected earlier in the kink-scattering processes in the nontopological sector.