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High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract:
In this paper, we have studied the kink and antikink solutions in several
neutral scalar models in 1+1 dimension. We follow the standard approach to
write down the leading order and the second order force between long distance
separated kink and antikink. The leading order force is proportional to
exponential decay with respect to the distance between the two nearest kinks or
antikinks. The second order force have a similar behavior with the larger decay
factor, namely $3\over 2$. We make use of these properties to construct the
kink lattice. The dynamics of the kink lattice with leading order force can be
identified as ordinary nonperiodic Toda lattice. Also the periodic Toda lattice
can be obtained when the number of kink lattice is even. The system of kink
lattice with force up to the next order corresponds to a new specific
deformation of Toda lattice system. There is no well study on this deformation
in the integrable literatures.We found that the deformed Toda system are near
integrable system, since the integrability are hindered by high order
correction terms. Our work provides a effective theory for kink interactions
and a new near or quasi integrable model.
