# Kink-Kink and Kink-Antikink Interactions with Long-Range Tails

## Abstract

In this Letter, we address the long-range interaction between kinks and antikinks, as well as kinks and kinks, in φ^{2n+4} field theories for n > 1. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the 2n/(n–1)th power of their separation, and we identify the general prefactor for *arbitrary n*. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of n = 2 (φ^{8} model), n = 3 (φ^{10} model), and n = 4 (φ^{12} model).

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1510543

- Alternate Identifier(s):
- OSTI ID: 1532709

- Report Number(s):
- LA-UR-18-30946

Journal ID: ISSN 0031-9007; PRLTAO; 171601

- Grant/Contract Number:
- 02.a03.21.0005; 89233218CNA000001

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 122 Journal Issue: 17; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics

### Citation Formats

```
Christov, Ivan C., Decker, Robert J., Demirkaya, A., Gani, Vakhid A., Kevrekidis, P. G., Khare, Avinash, and Saxena, Avadh. Kink-Kink and Kink-Antikink Interactions with Long-Range Tails. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.122.171601.
```

```
Christov, Ivan C., Decker, Robert J., Demirkaya, A., Gani, Vakhid A., Kevrekidis, P. G., Khare, Avinash, & Saxena, Avadh. Kink-Kink and Kink-Antikink Interactions with Long-Range Tails. United States. doi:10.1103/PhysRevLett.122.171601.
```

```
Christov, Ivan C., Decker, Robert J., Demirkaya, A., Gani, Vakhid A., Kevrekidis, P. G., Khare, Avinash, and Saxena, Avadh. Fri .
"Kink-Kink and Kink-Antikink Interactions with Long-Range Tails". United States. doi:10.1103/PhysRevLett.122.171601.
```

```
@article{osti_1510543,
```

title = {Kink-Kink and Kink-Antikink Interactions with Long-Range Tails},

author = {Christov, Ivan C. and Decker, Robert J. and Demirkaya, A. and Gani, Vakhid A. and Kevrekidis, P. G. and Khare, Avinash and Saxena, Avadh},

abstractNote = {In this Letter, we address the long-range interaction between kinks and antikinks, as well as kinks and kinks, in φ2n+4 field theories for n > 1. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the 2n/(n–1)th power of their separation, and we identify the general prefactor for arbitrary n. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of n = 2 (φ8 model), n = 3 (φ10 model), and n = 4 (φ12 model).},

doi = {10.1103/PhysRevLett.122.171601},

journal = {Physical Review Letters},

number = 17,

volume = 122,

place = {United States},

year = {2019},

month = {5}

}

DOI: 10.1103/PhysRevLett.122.171601

*Citation information provided by*

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Web of Science

#### Figures / Tables:

*a*as a function of

*A*for the kink-kink interaction (blue) and kinkantikink interaction (red) in the φ

^{8}model. The dashed lines are computed numerically, and the solid lines are computed analytically. Top right is the plotmore »

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*