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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Integrability of a Time Dependent Coupled Harmonic Oscillator in Higher Dimensions

Discontinuity, Nonlinearity, and Complexity 7(1) (2018) 81--94 | DOI:10.5890/DNC.2018.03.007

Ram Mehar Singh$^{1}$, S B Bhardwaj$^{2}$, Kushal Sharma$^{3}$, Richa Rani$^{2}$, Fakir Chand$^{2}$, Anand Malik$^{4}$

$^{1}$ Department of Physics, Chaudhary Devi Lal University Sirsa-125055, India

$^{2}$ Department of Physics, Kurukshetra University Kurukshetra-136119, India

$^{3}$ Department of Mathematics, National Institute of Technology, Hamirpur-177005, India

$^{4}$ Department of Physics, Chaudhary Bansi Lal University, Bhiwani-127021, India

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Within the frame work of extended complex phase space characterized by x = x1 + ip4,y = x2 + ip5,z = x3 + ip6, px = p1 + ix4, py = p2 + ix5 and pz = p3 +ix6, we investigate the exact dynamical invariant for a coupled harmonic system in three dimensions. For this purpose Lie-algebraic method is employed and the invariant obtained in this work may play an important role in reducing the order of differential equations, solution of Cauchy system and to check the accuracy of a numerical simulation.


The authors are thankful to the learned referees for several useful comments which helped in considerably improving and fine-tuning some of the ideas in the original version of the paper.


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