Abstract
In the present paper, the nonlinear interaction between Langmuir waves and ion acoustic waves described by the onedimensional Zakharov equations (ZEs) for relativistic plasmas are investigated formulating a low dimensional model. Equilibrium points of the model are found and it is shown that the existence and stability conditions of the equilibrium point depend on the relativistic parameter. Computational investigations are carried out to examine the effects of relativistic parameter and other plasma parameters on the dynamics of the model. Power spectrum analysis using fast fourier transform and also construction of first return map confirm that periodic, quasiperiodic, and chaotic type solution exist for both relativistic as well as in nonrelativistic case. Existence of supercritical Hopf bifurcation is noted in the system for two critical plasmon numbers.
We are grateful to Editors and the anonymous referee for their critical comments and suggestions, which have immensely improved the content and presentation of the paper.
I. INTRODUCTION
II. THEORETICAL MODEL
III. NONLINEAR ANALYSIS AND NUMERICAL SIMULATION RESULTS
IV. CONCLUSION
Key Topics
 Relativistic plasmas
 12.0
 Plasma waves
 8.0
 Bifurcations
 6.0
 Time series analysis
 6.0
 Electrostatic waves
 5.0
Figures
Phase portraits of the given system for different values of k: (a) periodic (k = 0.01); (b)quasiperiodic (k = 0.3); keeping the value and N = 1.5 fixed.
Phase portraits of the given system for different values of k: (a) periodic (k = 0.01); (b)quasiperiodic (k = 0.3); keeping the value and N = 1.5 fixed.
phase portraits of the given system for different values of k: (a) Quasiperiodic (k = 0.8); (b) chaotic (k = 1.3); keeping the value and N = 1.5 fixed.
phase portraits of the given system for different values of k: (a) Quasiperiodic (k = 0.8); (b) chaotic (k = 1.3); keeping the value and N = 1.5 fixed.
(a) Power spectrum of time series data of n 1 using FFT and (b) Return map of n 1 are constructed for , and N = 1.5.
(a) Power spectrum of time series data of n 1 using FFT and (b) Return map of n 1 are constructed for , and N = 1.5.
(a) Power spectrum of time series data of n 1 using FFT and (b) Return map of n 1 are shown for , and N = 1.5.
(a) Power spectrum of time series data of n 1 using FFT and (b) Return map of n 1 are shown for , and N = 1.5.
(a) Power spectrum of time series data of n 1 using FFT and (b) Return map of n 1 are plotted for , and N = 1.5.
(a) Power spectrum of time series data of n 1 using FFT and (b) Return map of n 1 are plotted for , and N = 1.5.
Phase portraits of the given system for different values of N: (a) chaotic (N = 0.5); (b) quasiperiodic (N = 1.0) keeping the value and k = 0.8 fixed.
Phase portraits of the given system for different values of N: (a) chaotic (N = 0.5); (b) quasiperiodic (N = 1.0) keeping the value and k = 0.8 fixed.
(a) Power spectrum of time series data of a using FFT and (b) Return map of a are presented for , and N = 0.5.
(a) Power spectrum of time series data of a using FFT and (b) Return map of a are presented for , and N = 0.5.
(a) Power spectrum of time series data of a using FFT and (b) Return map of a are plotted for , and N = 1.0.
(a) Power spectrum of time series data of a using FFT and (b) Return map of a are plotted for , and N = 1.0.
Phase portraits of the given system for different values of N: (a) quasiperiodic (N = 0.5); (b) quasiperiodic (N = 1.0) keeping the value and k = 0.5 fixed.
Phase portraits of the given system for different values of N: (a) quasiperiodic (N = 0.5); (b) quasiperiodic (N = 1.0) keeping the value and k = 0.5 fixed.
(a) Power spectrum of time series data of using FFT and (b) Return map of are drawn for , and N = 0.5.
(a) Power spectrum of time series data of using FFT and (b) Return map of are drawn for , and N = 0.5.
(a) Power spectrum of time series data of using FFT and (b) Return map of are drawn for , and N = 1.0.
(a) Power spectrum of time series data of using FFT and (b) Return map of are drawn for , and N = 1.0.
Phase portraits of the given system for different values of : (a) ; (b) ; keeping the value k = 0.8 and N = 1.5 fixed.
Phase portraits of the given system for different values of : (a) ; (b) ; keeping the value k = 0.8 and N = 1.5 fixed.
(a) Power spectrum of time series data of using FFT and (b) Return map of are plotted for , and N = 1.5.
(a) Power spectrum of time series data of using FFT and (b) Return map of are plotted for , and N = 1.5.
(a) Power spectrum of time series data of using FFT and (b) Return map of are presented for , and N = 1.5.
(a) Power spectrum of time series data of using FFT and (b) Return map of are presented for , and N = 1.5.
MATCONT continuation diagram with respect to N for and K = 0.8.
MATCONT continuation diagram with respect to N for and K = 0.8.
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