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Self-focusing of a laser beam is one of the major consequences of nonlinear interaction of laser with plasma. In this paper, self-focusing of skew cosh Gaussian (skew-ChG) laser beam is studied in anisotropic, collisional plasma where in externally exponentially decreasing magnetic field is applied. Skewness parameters in the field profile of skew-ChG laser beam eventually determine intensity profile of the beam. The symmetry in skewness parameter in two transverse directions simplifies the calculations considerably. Second order, nonlinear, ordinary, coupled differential equations for Beam Width Parameters (BWP) are obtained using Akhmanovs approach under Wentzel–Kramers–Brillouin (WKB) and paraxial approximations which are solved numerically. For given amplitude of applied magnetic field, attenuated oscillatory self-focusing is observed with respect to change in attenuation coefficient.

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