Forces between kinks and antikinks with long-range tails

@article{Manton2019ForcesBK,
  title={Forces between kinks and antikinks with long-range tails},
  author={N. S. Manton},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2019}
}
  • N. Manton
  • Published 8 October 2018
  • Physics
  • Journal of Physics A: Mathematical and Theoretical
In a scalar field theory with a symmetric octic potential having a quartic minimum and two quadratic minima, kink solutions have long-range tails. We calculate the force between two kinks and between a kink and an antikink when their long-range tails overlap. This is a nonlinear problem, solved using an adiabatic ansatz for the accelerating kinks that leads to a modified, first-order Bogomolny equation. We find that the kink-kink force is repulsive and decays with the fourth power of the kink… 

Figures from this paper

Kink-Kink and Kink-Antikink Interactions with Long-Range Tails.
TLDR
It is found that the force of interaction decays with the 2n/(n-1)th power of their separation, and the general prefactor for arbitrary n is identified.
Collision of two kinks with inner structure
In this work, we study kink collisions in a scalar field model with scalar-kinetic coupling. This model supports kink/antikink solutions with inner structure in the energy density. The collision of
Kink–antikink interaction forces and bound states in a biharmonic ϕ 4 model
We consider the interaction of solitons in a biharmonic, beam model analogue of the well-studied $\phi^4$ Klein-Gordon theory. Specifically, we calculate the force between a well separated kink and
Interaction between kinks and antikinks with double long-range tails
Quasinormal modes in kink excitations and kink–antikink interactions: a toy model
We study excitations and collisions of kinks in a scalar field theory where the potential has two minima with $$Z_2$$Z2 symmetry. The field potential is designed to create a square well potential in
Family of potentials with power law kink tails
  • A. Khare, A. Saxena
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2019
We provide examples of a large class of one dimensional higher order field theories with kink solutions which asymptotically have a power-law tail either at one end or at both ends. We provide
Kinks in the relativistic model with logarithmic nonlinearity
We study the properties of a relativistic model with logarithmic nonlinearity. We show that such model allows two types of solutions: topologically trivial (gaussons) and topologically non-trivial
Non-topological kink scattering in a two-component scalar field theory model
Exotic final states in the $$\varphi ^8$$ multi-kink collisions
We study final states in the scattering of kinks and antikinks of the $$\varphi ^8$$ φ 8 field-theoretic model. We use the initial conditions in the form of two, three or four static or moving
Kink solutions in a generalized scalar φ 4 G field model
We study a scalar field model in a two dimensional space-time with a generalized ϕG4 potential which has four minima, obtaining novel kink solutions with well defined properties although the
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 17 REFERENCES
Force between Kinks with Long-range Tails
In a scalar field theory that has a symmetric octic potential with a quartic minimum and two quadratic minima, kink and mirror kink solutions have long-range tails. We calculate the force between
Kink-Kink and Kink-Antikink Interactions with Long-Range Tails.
TLDR
It is found that the force of interaction decays with the 2n/(n-1)th power of their separation, and the general prefactor for arbitrary n is identified.
Scattering of the φ8 kinks with power-law asymptotics
Analytical study of kinklike structures with polynomial tails
This work deals with models described by a single real scalar field in two-dimensional spacetime. The aim is to propose potentials that support massless minima and investigate the presence of
Long-range interactions of kinks
We present a computational analysis of the long-range interactions of solitary waves in higher-order field theories. Our vehicle of choice is the $\varphi^8$ field theory, although we explore similar
Successive phase transitions and kink solutions in ϕ(8), ϕ(10), and ϕ(12) field theories.
TLDR
It is found that the higher-order field theories have kink solutions with algebraically decaying tails and also asymmetric cases with mixed exponential-algebraic tail decay, unlike the lower-order ϕ (4) and ϕ(6) theories.
Soliton structures in P(φ) 2
We investigate general soliton features of a scalar field theory in two dimensions with polynomial self-interactions. The static solution and its linear fluctuations are discussed in general and
...
1
2
...