Propagation of nonlinear ion acoustic waves in a relativistic electron–ion plasma is studied using the covariant formulation. Ions are assumed cold and a polytropic equation of state of the form p = Cn^Γ is assumed for electrons with Γ = 1 (isothermal case). The continuity, momentum and energy equations for electrons and ions are transformed to a special frame of reference via Lorentz-transformation. In the said frame of reference, all physical quantities are time independent. The well-known Sagdeev potential (or pseudopotential) technique is used to investigate the effect of changes in polytropic index Γ, electron temperature T_e0 and phase speed of wave V_p on the wave amplitude. It is found that ion acoustic waves can propagate in the relativistic plasma only if the following condition (γ_V − eϕ/m_ic²)² > 1 is satisfied (where \(\gamma _{V} = 1/\sqrt{1 - V_{p}/c^{2}} \) is defined, ϕ is the electrostatic potential, m_i is the ion mass and c is the speed of light). Maximum value of the amplitude (\(\phi '_{m}\)) attained by the wave before collapsing, is also derived. It is also found that an increase in temperature T_e0 (or V_p) increases the maximum possible wave amplitude of the nonlinear wave whereas, increasing V_p results in decreasing \(\phi '_{m}\).

中文翻译：

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具有等温电子和冷离子的相对论等离子体中的非线性周期离子声波

使用协变公式研究了相对论电子离子等离子体中非线性离子声波的传播。离子被假定冷和形式的状态的多变方程p =道道^Γ假设用于与Γ= 1（等温的情况下）的电子。电子和离子的连续性，动量和能量方程式通过Lorentz变换转换为特殊的参考系。在所述参考框架中，所有物理量都是时间无关的。使用众所周知的Sagdeev势（或伪势）技术研究多变指数Γ，电子温度T _{e 0}和波V _p的相速度变化的影响在波幅上。据发现，离子声波可以相对论等离子体中传播仅当以下条件（γ _V - Eφ /中号_我Ç ²）² > 1的情况下（其中\（\ gamma _ {V} = 1 / \ sqrt {1-V_ {p} / c ^ {2}} \）被定义，φ是静电电位，中号_我是离子质量和Ç是光的速度）。振幅最大值（\（\ phi'_ {m} \）也推导了波浪在坍塌之前达到的 还发现温度T _{e 0}（或V _p）的增加会增加非线性波的最大可能波幅，而V _p的增加会导致非线性波的减小\（\ phi'_ {m} \）。