In the theoretical investigation of the self-focusing of elegant Hermite–Cosh–Gaussian (EHChG) beams, the crucial role of decentered parameters has been explored thoroughly in the case of the weak relativistic and ponderomotive regime of interaction. In the present study, the Cartesian coordinate system has been employed, which enables us to study the evolution of two transverse beam-width parameters simultaneously. The differential equations for the beam-width parameters are set up through the parabolic wave equation approach by following WKB and paraxial approximations.

中文翻译：

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弱相对论和动力作用下等离子体中厄米-科什-高斯激光束的自聚焦

在对优雅的Hermite-Cosh-Gaussian（EHChG）梁的自聚焦进行的理论研究中，在弱相对论和质动力相互作用的情况下，对偏心参数的关键作用进行了深入研究。在本研究中，采用了笛卡尔坐标系，这使我们能够同时研究两个横向波束宽度参数的演变。光束宽度参数的微分方程是通过抛物线波方程方法，遵循WKB和近轴近似来建立的。