The nonlinear Riemann wave equations (RWEs) and the Landau-Ginsburg-Higgs (LGH) equation are related to plasma electrostatic waves, ion-cyclotron wave electrostatic potential, superconductivity, and drift coherent ion-cyclotron waves in centrifugally inhomogeneous plasma. In this article, the interactions between the maximum order linear and nonlinear factors are balanced to compute realistic soliton solutions to the formerly stated equations in terms of hyperbolic functions. The linear and nonlinear effects rheostat the structure of the wave profiles, which vary in response to changes in the subjective parameters combined with the solutions. The established solutions to the aforementioned models using the extended tanh scheme are descriptive, typical, and consistent, and include standard soliton shapes such as bright soliton, dark soliton, compacton, peakon, periodic, and others that can be used to analyze in ion-acoustic and magneto-sound waves in plasma, homogeneous, and stationary media, particularly in the propagation of tidal and tsunami waves.

非线性黎曼波动方程 (RWE) 和 Landau-Ginsburg-Higgs (LGH) 方程与离心非均匀等离子体中的等离子体静电波、离子-回旋波静电势、超导性和漂移相干离子-回旋波有关。在本文中，最大阶线性因素和非线性因素之间的相互作用得到平衡，以根据双曲函数计算先前所述方程的实际孤子解。线性和非线性效应变阻器波形的结构，其随着与解决方案结合的主观参数的变化而变化。使用扩展 tanh 方案对上述模型建立的解决方案是描述性的、典型的和一致的，包括标准孤子形状，如亮孤子、暗孤子、