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On invariant analysis and conservation laws for degenerate coupled multi-KdV equations for multiplicity \(l = 3\)

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Abstract

The degenerate coupled multi-Korteweg–de Vries equations for coupled multiplicity \(l=3\) are studied. The equations, also known as three-field Kaup–Boussinesq equations, are considered for invariant analysis and conservation laws. The classical Lie’s symmetry method is used to analyse the symmetries of equations. Based on the Killing’s form, which is invariant of adjoint action, the full classification for Lie algebra is presented. Further, one-dimensional optimal group classification is used to obtain invariant solutions. Besides this, using general theorem proved by Ibragimov, we find several non-local conservation laws for these equations. The conserved currents obtained in this work can be useful for the better understanding of some physical phenomena modelled by the underlying equations.

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Acknowledgements

Rajesh Kumar Gupta is grateful to the University Grants Commission for sponsoring this research under Research Award Scheme (F. 30-105 / 2016 (SA-II)).

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Authors and Affiliations

  1. Centre for Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, 151 001, India

    R K Gupta

  2. Yadavindra College of Engineering, Punjabi University, Guru Kashi Campus, Talwandi, Sabo, 151 302, India

    Manjit Singh

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  1. R K Gupta
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  2. Manjit Singh
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Correspondence to Manjit Singh.

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Gupta, R.K., Singh, M. On invariant analysis and conservation laws for degenerate coupled multi-KdV equations for multiplicity \(l = 3\). Pramana - J Phys 92, 70 (2019). https://doi.org/10.1007/s12043-019-1730-6

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  • DOI: https://doi.org/10.1007/s12043-019-1730-6

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