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Breather structures in degenerate relativistic non-extensive plasma

Published online by Cambridge University Press:  15 May 2017

M. Shahmansouri*
Affiliation:
Department of Physics, Faculty of Science, Arak University, Arak, PO Box 38156-8-8349, Iran
H. Alinejad
Affiliation:
Department of Physics, Faculty of Basic Science, Babol Noshirvani University of Technology, Babol 47148-71167, Iran
M. Tribeche
Affiliation:
Faculty of Physics, Theoretical Physics Laboratory, Plasma Physics Group, University of Bab-Ezzouar, USTHB, B.P. 32, El Alia, Algiers 16111, Algeria
*
Email address for correspondence: mshmansouri@gmail.com

Abstract

We examine the excitation of breather structures in a degenerate relativistic plasma consisting of non-extensive electrons and cold ions. For this purpose, the multiple time scale perturbation technique is used to obtain a nonlinear Schrödinger equation (NLSE). We then consider different localized solutions regarding analytical breather solutions of the NLSE, and examine their properties in the frame of the present plasma system, i.e. a degenerate relativistic non-extensive plasma. The results of the present investigation may be useful for the understanding of the basic features of the nonlinear excitations that may occur in dense astrophysical plasmas.

Type
Research Article
Copyright
© Cambridge University Press 2017 

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References

Akhmediev, N. N., Eleonskii, V. M. & Kulagin, N. E. 1987 Exact first-order solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 72, 809.Google Scholar
Akhtar, N., El-Taibany, W. F. & Mahmood, S. 2013 Electrostatic double layers in a warm negative ion plasma with nonextensive electrons. Phys. Lett. A 377, 1282.Google Scholar
Akhtar, N., El-Taibany, W. F., Mahmood, S., Behery, E. E., Khan, S. A., Ali, S. & Hussain, S. 2015 Transverse instability of ion acoustic solitons in a magnetized plasma including-nonextensive electrons and positrons. J. Plasma Phys. 81, 905810518.CrossRefGoogle Scholar
Alinejad, H., Mahdavi, M. & Shahmansouri, M. 2014 Modulational instability of ion-acoustic waves in a plasma with two-temperature kappa-distributed electrons. Astrophys. Space Sci. 352, 571.CrossRefGoogle Scholar
Alinejad, H., Mahdavi, M. & Shahmansouri, M. 2016 Weakly dissipative dust-ion acoustic wave modulation. J. Plasma Phys. 82, 905820104.CrossRefGoogle Scholar
Alinejad, H. & Shahmansouri, M. 2012 Low intensity dust ion-acoustic shock waves due to dust charge fluctuation in a nonextensive dusty plasma. Phys. Plasmas 19, 083705.Google Scholar
Ashraf, S., Yasmin, S., Asaduzzaman, M. & Mamun, A. A. 2014 Electrostatic solitary structures in a magnetized nonextensive plasma with q-distributed electrons. Plasma Phys. Report 40, 306.CrossRefGoogle Scholar
Bacha, M., Boukhalfa, S. & Tribeche, M. 2012 Ion-acoustic rogue waves in a plasma with a $q$ -nonextensive electron velocity distribution. Astrophys Space Sci. 341, 591.CrossRefGoogle Scholar
Bailung, H., Sharma, S. K. & Nakamura, Y. 2011 Observation of Peregrine solitons in a multicomponent plasma with negative ions. Phys. Rev. Lett. 107, 255005.Google Scholar
Bains, A. S., Li, B. & Tribeche, M. 2013 Envelope excitations in electronegative plasmas with electrons featuring the Tsallis distribution. Phys. Plasmas 20, 092119.CrossRefGoogle Scholar
Bains, A. S., Tribeche, M., Saini, N. S. & Gill, T. S. 2017 Modulation instability and rogue wave structures of positron-acoustic waves in q-nonextensive plasmas. Physica A 466, 111.CrossRefGoogle Scholar
Behery, E. E., Selim, M. M. & El-Taibany, W. F. 2015 Nonplanar dynamics of variable size dust grains in nonextensive dusty plasma. Phys. Plasmas 22, 112105.CrossRefGoogle Scholar
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. J. Fluid Mech. 27, 417.Google Scholar
Bludov, Y. V., Konotop, V. V. & Akhmediev, N. 2009 Matter rogue waves. Phys. Rev. A 80, 033610.Google Scholar
Bludov, Y. V., Konotop, V. V. & Akhmediev, N. 2010 Vector rogue waves in binary mixtures of Bose–Einstein condensates. Eur. Phys. J. ST 185, 169.CrossRefGoogle Scholar
Chabchoub, A., Hoffmann, N. & Akhmediev, N. 2011 Rogue wave observation in a water wave tank. Phys. Rev. Lett. 106, 204502.Google Scholar
Dauxois, T. & Peyrard, M. 2005 Physics of Solitons. Cambridge University Press.Google Scholar
Douglas, P., Bergamini, S. & Renzoni, F. 2006 Tunable Tsallis distributions in dissipative optical lattices. Phys. Rev. Lett. 96, 110601.CrossRefGoogle ScholarPubMed
Dubinova, I. B. & Dubinov, A. E. 2006 The theory of ion-sound solitons in plasma with electrons featuring the Tsallis distribution. Tech. Phys. Lett. 32, 575.Google Scholar
Dutta, P., Das, P. & Karmakar, P. K. 2016 Stability analysis of non-thermal complex astrofluids in the presence of polarized dust-charge fluctuations. Astrophys. Space Sci. 361, 322.Google Scholar
Dyson, F. J. & Lenard, A. 1967 Stability of matter. J. Math. Phys. 8, 423.CrossRefGoogle Scholar
Dysthe, K. B. & Trulsen, K. 1999 Note on breather type solutions of the NLS as models for freak-waves. Phys. Scr. T 82, 48.Google Scholar
El-Awady, E. L. & Moslem, W. M. 2011 On a plasma having nonextensive electrons and positrons: Rogue and solitary wave propagation. Phys. Plasmas 18, 082306.Google Scholar
El-Labany, S. K., El-Taibany, W. F. & Zedan, N. A. 2014 Instability of nonplanar modulated dust acoustic wave packets in a strongly coupled nonthermal dusty plasma. Phys. Plasmas 22, 073702.Google Scholar
El-Labany, S. K., Krim, M. S. A., El-Warraki, S. A. & El-Taibany, W. F. 2003 Modulational instability of a weakly relativistic ion acoustic wave in a warm plasma with nonthermal electrons. Chin. Phys. 12, 759.CrossRefGoogle Scholar
El-Shamy, E., Tribeche, M. & El-Taibany, W. F. 2014 The collisions of two ion acoustic solitary waves in a magnetized nonextensive plasma. Cent. Euro. J. Phys. 12, 805.Google Scholar
El-Taibany, W. F. & Kourakis, I. 2006 Modulational instability of dust acoustic waves in dusty plasmas: modulation obliqueness, background ion nonthermality, and dust charging effects. Phys. Plasmas 13, 062302.Google Scholar
El-Taibany, W. F. & Tribeche, M. 2012 Nonlinear ion-acoustic solitary waves in electronegative plasmas with electrons featuring Tsallis distribution. Phys. Plasmas 19, 024507.Google Scholar
El-Tantawy, S. A. 2016 Effect of ion viscosity on dust ion-acoustic shock waves in a nonextensive magnetoplasma. Astrophys. Space Sci. 361, 249.CrossRefGoogle Scholar
Eliasson, B. & Shukla, P. K. 2010 Numerical investigation of the instability and nonlinear evolution of narrow-band directional ocean waves. Phys. Rev. Lett. 105, 014501.CrossRefGoogle ScholarPubMed
Ferdousi, M., Miah, M. R., Sultana, S. & Mamun, A. A. 2015 Dust-acoustic shock waves in an electron depleted nonextensive dusty plasma. Astrophys. Space Sci. 360, 43.CrossRefGoogle Scholar
Feron, C. & Hjorth, J. 2008 Simulated dark-matter halos as a test of nonextensive statistical mechanics. Phys. Rev. E 77, 022106.Google Scholar
Gell-Mann, M. & Tsallis, C. 2004 Nonextensive Entropy-Interdisciplinary Applications. Oxford University Press.Google Scholar
Gervino, G., Lavagno, A. & Pigato, D. 2012 Nonextensive statistical effects in the quark–gluon plasma formation at relativistic heavy-ion collisions energies. Cent. Euro. J. Phys. 10, 594.Google Scholar
Haug, H. & Koch, S. W. 2004 Quantum Theory of the Optical and Electronic Properties of Semiconductors. World Scientific.Google Scholar
Hossen, M. R., Ema, S. A. & Mamun, A. A. 2016 Small amplitude dust–electron-acoustic shock waves and double layers in a nonextensive complex plasma with viscous electron fluids. IEEE Trans. Plasma Sci. 44, 492.Google Scholar
Hoyos, J., Reisenegger, A. & Valdivia, J. A. 2008 Magnetic field evolution in neutron stars: one-dimensional multi-fluid model. Astron. Astrophys. 487, 789.Google Scholar
Kharif, C., Pelinovsky, E. & Slunyaev, A. 2009 Rogue Waves in the Ocean. Springer.Google Scholar
Kibler, B., Fatome, J., Finot, C., Millot, G., Dias, F., Genty, G., Akhmediev, N. & Dudley, J. M. 2010 Observation of Kuznetsov–Ma soliton dynamics in optical fibre. Nature Phys. A 6, 790.Google Scholar
Kourakis, I., McKerr, M. & Ur-Rahman, A. 2013 Semiclassical relativistic fluid theory for electrostatic envelope modes in dense electron–positron–ion plasmas: modulational instability and rogue waves. J. Plasma Phys. 79, 1089.Google Scholar
Kuznetsov, E. 1977 Solitons in a parametrically unstable plasma. Sov. Phys. Dokl. 22, 507.Google Scholar
Lavagno, A. & Pigato, D. 2011 Nonextensive statistical effects in protoneutron stars. Eur. Phys. J. A 47, 52.Google Scholar
Lima, J. A. S., Silva, R. & Plastino, A. R. 2001 Nonextensive thermostatistics and the $H$ theorem. Phys. Rev. Lett. 86, 2938.Google Scholar
Liolios, T. E. 2003 Screened $\unicode[STIX]{x1D6FC}$ decay in dense astrophysical plasmas and superstrong magnetic fields. Phys. Rev. C 68, 015804.CrossRefGoogle Scholar
Liu, B. & Goree, J. 2008 Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma. Phys. Rev. Lett. 100, 5.CrossRefGoogle Scholar
Ma, Y. 1979 The perturbed plane-wave solutions of the cubic Schrödinger equation. Stud. Appl. Maths 60, 43.Google Scholar
Marklund, M. & Stenflo, L. 2009 Exciting rogue waves. Physics 2, 86.Google Scholar
Martinenko, E. & Shivamoggi, B. K. 2004 Thomas–Fermi model: nonextensive statistical mechanics approach. Phys. Rev. A 69, 52504.Google Scholar
Michel, F. C. 1982 Theory of pulsar magnetospheres. Rev. Mod. Phys. 54, 1.CrossRefGoogle Scholar
Moslem, W. M. 2011 Langmuir rogue waves in electron–positron plasmas. Phys. Plasmas 18, 032301.Google Scholar
Moslem, W. M., Shukla, P. K. & Eliasson, B. 2011 Surface plasma rogue waves. Eur. Phys. Lett. 96, 25002.Google Scholar
Osborne, A. R. 2009 Nonlinear Ocean Waves. Academic.Google Scholar
Ourabah, K. & Tribeche, M. 2014 Relativistic formulation of the generalized nonextensive Thomas–Fermi model. Physica A 393, 470.Google Scholar
Peregrine, D. H. 1983 Water waves, nonlinear Schrodinger equations and their solutions. J. Austral. Math. Soc. B 25, 16.Google Scholar
Pickup, R. M., Cywinski, R., Pappas, C., Faragao, B. & Fouquet, P. 2009 Generalized spin-glass relaxation. Phys. Rev. Lett. 102, 097202.Google Scholar
Plastino, A. R. & Plastino, A. 1993 Stellar polytropes and Tsallis’ entropy. Phys. Lett. A 174, 384.CrossRefGoogle Scholar
Rahman, A. & Ali, S. 2014 Solitary and rogue waves in Fermi–Dirac plasmas: relativistic degeneracy effects. Astrophys. Space Sci. 351, 165.CrossRefGoogle Scholar
Rahman, A., Kerr, M. Mc., El-Taibany, W. F., Kourakis, I. & Qamar, A. 2015 Amplitude modulation of quantum-ion-acoustic wavepackets in electron–positron–ion plasmas: modulational instability, envelope modes, extreme waves. Phys. Plasmas 22, 022305.Google Scholar
Ruban, V., Kodama, Y. & Ruderman, M. 2010 Rogue waves – towards a unifying concept? Discussions and debates. Eur. Phys. J. Spec. Top. 185, 5.Google Scholar
Saha, A. 2017 Nonlinear excitations for the positron acoustic shock waves in dissipative nonextensive electron–positron–ion plasmas. Phys. Plasmas 24, 034502.CrossRefGoogle Scholar
Saha, A. & Chatterjee, P. 2015a Qualitative structures of electron-acoustic waves in an unmagnetized plasma with q-nonextensive hot electrons. Eur. Phys. J. Plus 130, 222.Google Scholar
Saha, A. & Chatterjee, P. 2015b Solitonic, periodic, quasiperiodic and chaotic structures of dust ion acoustic waves in nonextensive dusty plasmas. Eur. Phys. J. D 69, 203.Google Scholar
Saini, N. S. & Misra, A. P. 2015 Modulation of ion-acoustic waves in a nonextensive plasma with two-temperature electrons. Phys. Plasmas 22, 092124.Google Scholar
Shahmansouri, M. & Alinejad, H. 2013a Arbitrary amplitude electron acoustic waves in a magnetized nonextensive plasma. Astrophys. Space Sci. 347, 305.CrossRefGoogle Scholar
Shahmansouri, M. & Alinejad, H. 2013b Effect of electron nonextensivity on oblique propagation of arbitrary ion acoustic waves in a magnetized plasma. Astrophys. Space Sci. 347, 305.Google Scholar
Shahmansouri, M. & Alinejad, H. 2015 The polarized Debye sheath effect on Kadomtsev-Petviashvili electrostatic structures in strongly coupled dusty plasma. Phys. Plasmas 22, 043704.CrossRefGoogle Scholar
Shahmansouri, M & Borhanian, J. 2013 Spherical Kadomtsev–Petviashvili solitons in a suprathermal complex plasma. Comm. Theor. Phys. 60, 227.Google Scholar
Shahmansouri, M. & Farokhi, B. 2012 Nonlinear theory of longitudinal dust-lattice wave in a magnetic dusty plasma crystal. J. Plasma Phys. 78, 259.Google Scholar
Shahmansouri, M. & Misra, A. P. 2016 Modulation and nonlinear evolution of multi-dimensional Langmuir wave envelopes in a relativistic plasma. Phys. Plasmas 23, 122112.Google Scholar
Shahmansouri, M. & Tribeche, M. 2012 Arbitrary amplitude dust acoustic waves in a nonextensive dusty plasma. Astrophys. Space Sci. 344, 99.Google Scholar
Shahmansouri, M. & Tribeche, H. 2013 Nonextensive dust acoustic shock structures in complex plasmas. Astrophys. Space Sci. 346, 165.Google Scholar
Shapiro, S. L. & Teukolsky, S. A. 1983 Black Holes, White Dwarfs and Neutron Stars. Wiely.Google Scholar
Shrira, V. I. & Geogjaev, V. V. 2010 What make the Peregrine soliton so special as a prototype of freak waves? J. Engng Maths 67, 11.Google Scholar
Shukla, P. K., Kourakis, I. & Eliasson, B. 2006 Instability and evolution of nonlinearly interacting water waves. Phys. Rev. Lett. 97, 094501.Google Scholar
Silva, R., Plastino, A. R. & Lima, J. A. S. 1998 A Maxwellian path to the q-nonextensive velocity distribution function. Phys. Lett. A 249, 401.CrossRefGoogle Scholar
Solli, D. R., Ropers, C., Koonath, P. & Jalali, B. 2007 Optical rogue waves. Nature 450, 1054.CrossRefGoogle ScholarPubMed
Spruch, L. 1991 Pedagogic notes on Thomas–Fermi theory (and on some improvements): atoms, stars, and the stability of bulk matte. Rev. Mod. Phys. 63, 151.Google Scholar
Stenflo, L. & Marklund, M. 2010 Rogue waves in the atmosphere. J. Plasma Phys. 76, 293.Google Scholar
Tandberg-Hansen, E. & Emslie, A. G. 1988 The Physics of Solar Flares. Cambridge University Press.Google Scholar
Taniutiand, T. & Yajima, N. 1969 Perturbation method for a nonlinear wave modulation. J. Math. Phys. 10, 1369.CrossRefGoogle Scholar
Tribeche, M., Djebarni, L. & Amour, R. 2010 Ion-acoustic solitary waves in a plasma with a $q$ -nonextensive electron velocity distribution. Phys. Plasmas 17, 042114.Google Scholar
Tsallis, C. 1988 Possible generalization of Boltzmann–Gibbs statistics. J. Stat. Phys. 52, 479.Google Scholar
Tsallis, C. 2001 Nonextensive statistical mechanics and thermodynamics. In Lecture Notes in Physics (ed. Abe, S. & Okamoto, Y.). Springer.Google Scholar
Tsallis, C., Mendes, R. & Plastino, A. R. 1998 The role of constraints within generalized nonextensive statistics. Physica A 261, 534.Google Scholar
Tsallis, C., Prato, D. & Plastino, A. R. 2004 Nonextensive statistical mechanics: some links with astronomical phenomena. Astrophys. Space Sci. 290, 259.Google Scholar
Veldes, G., Borhanian, J., McKerr, M., Saxena, V., Frantzeskakis, D. J. & Kourakis, I. 2013 Electromagnetic rogue waves in beam–plasma interactions. J. Opt. 15, 064003.Google Scholar