Nonlinear shock waves in plasma was modeled and studied using Ramani equation of sixth order and its coupled form representing the interaction between two waves. A new combined methodology of both Lie infinitesimal transformation and singular manifold methods was exploited to create analytical solutions. The method was extended to investigate a coupled system of evolution equations as same as a single evolution equation. Soliton solutions were created for both models.

中文翻译：

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等离子体波演化和传播由六阶拉马尼和使用对称方法的耦合拉马尼方程建模

使用六阶拉马尼方程及其表示两个波之间相互作用的耦合形式对等离子体中的非线性冲击波进行建模和研究。利用李无穷小变换和奇异流形方法的新组合方法来创建解析解。该方法被扩展到研究一个与单个演化方程相同的演化方程耦合系统。为这两种模型都创建了孤子解决方案。