Conservation Laws for the Nonlinear Klein-Gordon Equation in (1+1)-, (2+1), and (3+1)-dimensions

• Published in: arXiv.org
• Main Author: Muhammad Al-Zafar Khan
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 16.05.2023
• Subjects: Conservation laws; Klein-Gordon equation; Solitary waves; Traveling waves; Trigonometric functions

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 norma...