Article citationsMore>>

Kowalczyk, M., Martel, Y. and Muñoz, C. (2017) Kink Dynamics in the ∅⁴ Model: Asymptotic Stability for Odd Perturbations in the Energy Space. Journal of the American Mathematical Society, 30, 769-798.
https://doi.org/10.1090/jams/870

has been cited by the following article:

• TITLE: Exact Topological Soliton Solutions to the Strongly Perturbed Family of Sine-Gordon Type Equations

  AUTHORS: Stephen Johnson, Essaid Zerrad, Sokratis Makrogiannis, Jun Ren

  KEYWORDS: Topological Soliton, Kink Soliton, Sine-Gordon Equation, Dispersion, Perturbation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.10, October 22, 2019

  ABSTRACT: This paper uses the Ansatz method to solve for exact topological soliton solutions to sine-Gordon type equations. Single, double, and triple sine-Gordon and sine-cosine-Gordon equations are investigated along with dispersive and highly dispersive variations. After these solutions are found, strong perturbations are added to each equation and the new solutions are found. In solving both the perturbed and unperturbed sine-Gordon type equations, constraints are imposed on the parameters. The novel contributions of the authors are the soliton solutions to the strongly perturbed sine-Gordon equation and its variations. These results are important to the study of Josephson junctions, crystal dislocations, ultra-short optical pulses, relativistic field theory, and elementary particles.