 [2305.11180] Conservation Laws for the Nonlinear Klein-Gordon Equation in (1+1)-, (2+1), and (3+1)-dimensions




























  








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Nonlinear Sciences > Pattern Formation and Solitons


arXiv:2305.11180 (nlin)
    




  [Submitted on 16 May 2023]
Title:Conservation Laws for the Nonlinear Klein-Gordon Equation in (1+1)-, (2+1), and (3+1)-dimensions
Authors:Muhammad Al-Zafar Khan View a PDF of the paper titled Conservation Laws for the Nonlinear Klein-Gordon Equation in (1+1)-, (2+1), and (3+1)-dimensions, by Muhammad Al-Zafar Khan
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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.
    


 
Comments:
11 pages, 3 figures


Subjects:

Pattern Formation and Solitons (nlin.PS); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)

Cite as:
arXiv:2305.11180 [nlin.PS]


 
(or 
arXiv:2305.11180v1 [nlin.PS] for this version)
          
 
 

https://doi.org/10.48550/arXiv.2305.11180



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                arXiv-issued DOI via DataCite
              







Submission history From: Muhammad Al-Zafar Khan [view email]       [v1]
        Tue, 16 May 2023 10:22:47 UTC (1,696 KB)



 

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