相对论简并量子等离子体中完全非线性重离子声波行波解的动力学研究

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 496-506.

相对论简并量子等离子体中完全非线性重离子声波行波解的动力学研究

DestaLeta Temesgen^1,²,刘文军^1,*(),丁建¹

¹ 南京信息工程大学数学与统计学院南京 210044
² Department of Mathematics, Dilla University, P O Box 419, Dilla, Ethiopia

收稿日期:2019-08-02 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 刘文军 E-mail:wjliu@nuist.edu.cn
基金资助:
中国科学技术部国际杰青计划(Ethiopia-18-010);国家自然科学基金(11950410502);国家自然科学基金(11771216);江苏省六大人才高峰计划(2015-XCL-020)

Dynamics of Traveling Wave Solutions to Fully Nonlinear Heavy Ion-Acoustic Degenerate Relativistic Quantum Plasmas

Leta Temesgen Desta^1,²,Wenjun Liu^1,*(),Jian Ding¹

¹ School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044
² Department of Mathematics, Dilla University, P O Box 419, Dilla, Ethiopia

Received:2019-08-02 Online:2021-04-26 Published:2021-04-29
Contact: Wenjun Liu E-mail:wjliu@nuist.edu.cn
Supported by:
the Talented Young Scientist Program of Ministry of Science and Technology of China(Ethiopia-18-010);the NSFC(11950410502);the NSFC(11771216);the Six Talent Peaks Project in Jiangsu Province(2015-XCL-020)

摘要/Abstract

摘要：

基于离子声波模型的最新进展，研究了天体物理相对论简并量子等离子体（ADRQP）中完全非线性重离子声波（HIAWs）模型的动力学行为，以确定所有精确的显式行波解.为了保证上述解的存在性，确定了所有参数条件.研究过程表明模型具有有界解（包括扭结和反扭结波解、周期峰解、伪峰解和紧解），这些结果改进了对该模型行波解的研究.

关键词: 孤波解, 周期峰, 紧性解, 扭波和反扭波, 伪峰, 分岔, 奇异行波系统

Abstract:

Based on recent advancements on ion-acoustic wave models, a fully nonlinear heavy ion-acoustic waves (HIAWs), in astrophysical degenerate relativistic quantum plasmas (ADRQP), which is studied by Sultana and Schlickeiser, is investigated. We study the dynamical behavior of the model to determine all exact explicit traveling wave solutions. To guarantee the existence of the aforementioned solutions, all parameter conditions are determined. Our procedure shows that the model has bounded solutions (including kink and anti-kink wave solutions, periodic peakon, pseudo-peakon wave solutions, and compact solutions). These results completely improve the study of traveling wave solutions for the mentioned model.

Key words: Solitary wave solution, Periodic peakon, Compacton, Kink and anti-kink wave, Pseudo-peakon, Bifurcation, Singular traveling wave system

中图分类号:

O175.2

DestaLeta Temesgen,刘文军,丁建. 相对论简并量子等离子体中完全非线性重离子声波行波解的动力学研究[J]. 数学物理学报, 2021, 41(2): 496-506.

Leta Temesgen Desta,Wenjun Liu,Jian Ding. Dynamics of Traveling Wave Solutions to Fully Nonlinear Heavy Ion-Acoustic Degenerate Relativistic Quantum Plasmas[J]. Acta mathematica scientia,Series A, 2021, 41(2): 496-506.

参考文献

1	Marklund M , Shukla P K . Nonlinear collective effects in photon-photon and photon-plasma interactions. Rev Mod Phys, 2006, 78, 591- 640
2	Fortov V E . Extreme states of matter on Earth and in space. Physics Uspekhi, 2009, 52, 615- 647
3	Drake R P . Perspectives on high-energy-density physics. Phys Plasmas, 2009, 16, 00555017
4	Chandrasekhar S . Dynamical instability of gaseous masses approaching the Schwarzschild limit in general relativity. Phys Rev Lett, 1964, 12, 114- 116
5	Shapiro Stuart L , Teukolsky S A . Black holes, naked singularities and cosmic censorship. Amer Sci, 1991, 79, 330- 343
6	Chabrier G , Saumon D , Potekhin A Y . Dense Plasmas in astrophysics: from gaint planets to neuron stars. J Phys A: Math Gen, 2006, 39, 4411- 4419
7	Masood W , Eliasson B . Electrostatic solitary waves in a quantum plasma with relativistically degenerate electrons. Phy Plasmas, 2011, 18, 034503
8	Roy N , Tasnim S , Mamun A . Solitary waves and double layers in an ultra-relativistic degenerate dusty electron-positron-ion plasma. Phys of Plasmas, 2012, 19, 033705
9	Rahman U , Ali S , Mushtaq A , Qamar A . Nonlinear ion acoustic excitations in relativistic degenerate, astrophysical electron-positron-ion plasmas. Plasma Phys, 2013, 79, 817- 823
10	Rahman U , Kourakis I , Qamar A . Electrostatic solitary waves in relativistic degenerate electron-positron-ion plasma. IEEE Trans Plasma Sci, 2015, 43, 974- 984
11	El-Labany S , El-Taibany F , El-Samahy E , et al. Ion acoustic solitary waves in degenerate electron-ion plasmas. IEEE Trans Plasma Sci, 2016, 44, 842- 848
12	Atteya A , Behery E E , El-Taibany W F . Ion acoustic shock waves in a degenerate relativistic plasma with nuclei of heavy elements. Eur Phys J Plus, 2017, 132, 109
13	Islam S , Sultana S , Mamun A A . Ultra-low frequency shock dynamics in degenerate relativistic plasmas. Phys Plasmas, 2017, 24, 092308
14	Mamun A , Amina M , Schlickeiser R . Heavy nucleus-acoustic spherical solitons in self-gravitating super-dense plasmas. Phys Plasmas, 2017, 24, 042307
15	Sultana S , Schlickeiser R . Fully nonlinear heavy ion-acoustic solitary waves in astrophysical degenerate relativistic quantum plasmas. Astrophys Space Sci, 2018, 363, 103
16	Sagdeev R Z . Cooperative phenomena and shock waves in collisionless plasmas. Rev plasma phys, 1966, 4, 23- 91
17	Osman M S . One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada-Kotera equation. Nonlinear Dyn, 2019, 96, 1491- 1496
18	Lendermann M , Koh J M , Tan J S , et al. Bifurcations and dynamical analysis of Coriolis-stabilized spherical lagging pendula. Nonlinear Dyn, 2019, 96, 921- 931
19	Li J , Chen G . On a class of singular nonlinear traveling wave equations. Internat J Bifur Chaos, 2007, 17, 4049- 4065
20	Li J . Singular Nonlinear Traveling Wave Equations: Bifurcations and Exact Solution. Beijing: Science Press, 2013
21	Malwe B H , Betchewe G , Doka S Y , et al. Travelling wave solutions and soliton solutions for the nonlinear transmission line using the generalized Riccati equation mapping method. Nonlinear Dyn, 2016, 84, 171- 177
22	An X L , Li Z . Dynamics analysis and Hamilton energy control of a generalized Lorenz system with hidden attractor. Nonlinear Dyn, 2018, 94, 2995- 3010
23	Byrd P F , Friedman M D . Handbook of Elliptic Integrals for Engineers and Scientists. Berlin: Springer, 1971
24	Li J , Zhu W , Chen G . Understanding peakons, periodic peakons and compactons via a shallow water wave equation. Internat J Bifur Chaos, 2016, 26, 1650207
25	Leta T D , Li J . Dynamical behavior and exact solution in invariant manifold for a septic derivative nonlinear Schr?dinger equation. Nonlinear Dyn, 2017, 89, 509- 529

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