An analytical model for the soliton-potential interaction is presented by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We find that the behavior of the soliton is like a point particle "living" under the influence of a complicated potential, that is a function of soliton velocity and the potential parameters. The analytic model does not have a clear prediction for the islands of initial velocities in which the soliton may reflect back or escape over the potential well.

By including a potential into the flat metric, we study the interaction of sine-Gordon soliton with different potentials. We will show numerically that while the soliton-barrier system shows fully classical behaviour, the soliton-well system demonstrates non-classical behaviour. In particular, solitons with low velocities are trapped in the well and radiate energy. Also for narrow windows of initial velocity, soliton reflects back from a potential well.

We study simultaneous collisions of two, three, and four kinks and antikinks of the φ 6 model at the same spatial point. Unlike the φ 4 kinks, the φ 6 kinks are asymmetric and this enriches the variety of the collision scenarios. In our numerical simulations we observe both reflection and bound state formation depending on the number of kinks and on their spatial ordering in the initial configuration. We also analyze the extreme values of the energy densities and the field gradient observed during the collisions. Our results suggest that very high energy densities can be produced in multi-kink collisions in a controllable manner. Appearance of high energy density spots in multi-kink collisions can be important in various physical applications of the Klein-Gordon model.

In this article, we present our global QCD analysis of leading neutron production in deep inelastic scattering at H1 and ZEUS collaborations. The analysis is performed in the framework of a perturbative QCD description for semi-inclusive processes, which is based on the fracture functions approach. Modeling the nonperturbative part of the fragmentation process at the input scale Q 2 0 , we analyze the Q 2 dependence of the leading neutron structure functions and obtain the neutron fracture functions (neutron FFs) from next-toleading order global QCD fit to data. We have also performed a careful estimation of the uncertainties using the "Hessian method" for the neutron FFs and corresponding observables originating from experimental errors. The predictions based on the obtained neutron FFs are in good agreement with all data analyzed, at small and large longitudinal momentum fraction x L as well as the scaled fractional momentum variable β.

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