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Solitons and conservation laws of Klein–Gordon equation with power law and log law nonlinearities

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Abstract

This paper obtains the conservation laws of the Klein–Gordon equation with power law and log law nonlinearities. The multiplier approach with Lie symmetry analysis is employed to obtain the conserved densities. The 1-soliton solutions are subsequently used to compute the conserved quantities from the conserved densities. Later the perturbation terms are added and the conservation laws of the perturbed Klein–Gordon equation are studied.

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Acknowledgements

The first and second authors (AB & AHK) are immensely grateful to King Fahd University of Petroleum and Minerals for sponsoring their academic visit to the university during December 2012.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Delaware State University, Dover, DE, 19901-2277, USA

    Anjan Biswas

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Anjan Biswas

  3. School of Mathematics, Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Johannesburg, Wits, 2050, South Africa

    Abdul H. Kara

  4. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Ashfaque H. Bokhari & F. D. Zaman

Authors
  1. Anjan Biswas
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  2. Abdul H. Kara
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  3. Ashfaque H. Bokhari
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  4. F. D. Zaman
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Correspondence to Anjan Biswas.

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Biswas, A., Kara, A.H., Bokhari, A.H. et al. Solitons and conservation laws of Klein–Gordon equation with power law and log law nonlinearities. Nonlinear Dyn 73, 2191–2196 (2013). https://doi.org/10.1007/s11071-013-0933-5

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  • DOI: https://doi.org/10.1007/s11071-013-0933-5

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