Conservation Laws for the Nonlinear Klein-Gordon Equation in (1+1)-, (2+1), and (3+1)-dimensions
Pattern Formation and Solitons
2023-05-22 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
We study soliton solutions to the Klein-Gordon equation via Lie symmetries and the travelling-wave ansatz. It is shown, by taking a linear combination of the spatial and temporal Lie point symmetries, that soliton solutions naturally exist, and the resulting field lies in the complex plane. We normalize the field over a finite spatial interval, and thereafter, specify one of the integration constants in terms of the other. Solutions to a specific type of nonlinear Klein-Gordon equation are studied via the sine-cosine method, and a real soliton wave is obtained. Lastly, the multiplier method is used to construct conservation laws for this particular nonlinear Klein-Gordon equation in (3 + 1)-dimensions.
Keywords
Cite
@article{arxiv.2305.11180,
title = {Conservation Laws for the Nonlinear Klein-Gordon Equation in (1+1)-, (2+1), and (3+1)-dimensions},
author = {Muhammad Al-Zafar Khan},
journal= {arXiv preprint arXiv:2305.11180},
year = {2023}
}
Comments
11 pages, 3 figures