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This paper studies the analytical and semi-analytic solutions of the generalized Calogero-Bogoyavlenskii-Schiff (CBS) equation.This model describes the (2 + 1)-dimensional interaction between Riemann-wave propagation along the y-axis and the x-axis wave.The extended simplest equation (ESE) method is applied to the model,and a variety of novel solitary-wave solutions is given.These solitary-wave solutions prove the dynamic behavior of soliton waves in plasma.The accuracy of the obtained solution is verified using a variational iteration(VI) semi-analytical scheme.The analysis and the match between the constructed analytical solution and the semi-analytical solution are sketched using various diagrams to show the accuracy of the solution we obtained.The adopted scheme\'s performance shows the effectiveness of the method and its ability to be applied to various nonlinear evolution equations.