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Wave-packet scattering off the kink-solution. (English) Zbl 1247.81551

Summary: We investigate the propagation of a wave-packet in the \(\Theta^4\) model. We solve the time-dependent equation of motion for two distinct initial conditions: The wave-packet in a trivial vacuum background and in the background of the kink soliton solution. We extract the scattering matrix from the wave-packet in the kink background at very late times and compare it with the result from static potential scattering in the small amplitude approximation. We vary the size of the initial wave-packet to identify nonlinear effects as, for example, the replacement of the center of the kink.

MSC:

81U05 \(2\)-body potential quantum scattering theory
35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
70S20 More general nonquantum field theories in mechanics of particles and systems
70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
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