Abstract
In this work, kink-antikink collision in a two-dimensional Lorentz-violating ϕ4 model is considered. It is shown that the Lorentz-violating term in the proposed model does not affect the structure of the linear perturbation spectrum of the standard ϕ4 model, and thus there exists only one vibrational mode. The Lorentz-violating term impacts, however, the frequency and spatial wave function of the vibrational mode. As a consequence, the well-known results on ϕ4 kink-antikink collision will also change. Collisions of kink-antikink pairs with different values of initial velocities and Lorentz-violating parameters are simulated using the Fourier spectral method. Our results indicate that models with larger Lorentz-violating parameters would have smaller critical velocities vc and smaller widths of bounce windows. Interesting fractal structures existing in the curves of maximal energy densities of the scalar field are also found.
Highlights
The domain wall is a simple type of topological soliton that exists in many nonlinear scalar field models
In the Lorentz-violating model, the width and energy density of a moving kink depend on both the magnitude and direction of its velocity because of breaking of time symmetry
Before the discussion of kink-antikink collision, it is important to study the linear perturbation of the static kink solution
Summary
The domain wall is a simple type of topological soliton that exists in many nonlinear scalar field models. It plays an important role in many branches of physics. If v0 lies in some narrow intervals below vc, one would observe the interesting n-bounce phenomenon; that is, after colliding n times, kinks escape rather than trapping into a bion [14, 15] These magical intervals are called n-bounce windows (nBWs), and have been found in many non-integrable models [16, 17]. Multikink collisions have been extensively studied recently [46, 47, 48, 49] All these works assume Lorentz invariance of their models.
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