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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 Coupled Harmonic Oscillator in Extended Complex Phase Space

Discontinuity, Nonlinearity, and Complexity 4(1) (2016) 35--48 | DOI:10.5890/DNC.2016.03.004

Ram Mehar Singh

Department of Physics, Ch. Devi Lal University, Sirsa-125055, Haryana, India

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With in the frame work of extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3 and py = p2 + ix4, we investigate the exact invariants for a coupled harmonic oscillator along with PT-symmetric version in two dimensions. For this purpose rationalization method is employed and the invariants obtained in this work play an important role to study the complex trajectories of the concerned classical system.


The author expresses his gratitude to Prof. S.C. Mishra and Dr. Fakir Chand, Department of Physics, Kurukshetra University, Kurukshetra (India), for their valuable suggestions regarding the manuscript. He is also thankful to the referees for their useful comments which helped in fine-tuning of some basic ideas in original version of the paper.


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