, 92:1 | Cite as

Group classification, conservation laws and Painlevé analysis for Klein–Gordon–Zakharov equations in (3\(+\)1)-dimension

  • Manjit SinghEmail author
  • R K Gupta


In this paper, we study Klein–Gordon–Zakharov equations which describe the propagation of strong turbulence of the Langmuir wave in a high-frequency plasma. Using the symbolic manipulation tool Maple, the classifications of symmetry algebra are carried out, and the construction of several local non-trivial conservation laws based on a direct method of Anco and Bluman is illustrated. Starting with determination of symmetry algebra, the one- and two-dimensional optimal systems are constructed, and optimality is also established using various invariant functions of full adjoint action. Apart from classification and construction of several conservation laws, the Painlevé analysis is also performed in a symbolic manner which describes the non-integrability of equations.


Klein–Gordon–Zakharov equations optimal systems conservation laws Painlevé analysis 


02.20.Qs 02.20.Sv 02.30.Jr 11.30.j 



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


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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Yadavindra College of EngineeringPunjabi UniversityTalwandi SaboIndia
  2. 2.Centre for Mathematics and Statistics, School of Basic and Applied SciencesCentral University of PunjabBathindaIndia

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