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In this paper, a generalized variable-coefficient KdV equation (vcKdV)arising in fluid mechanics, plasma physics and ocean dynamics is investigatedby using symmetry group analysis. Two basic generators are determined, and forevery generator in the optimal system the admissible forms of the coefficientsand the corresponding reduced ordinary differential equation are obtained. Thesearch for solutions to those reduced ordinary differential equations yieldsmany new solutions for the generalized vcKdV equation.

Two Similarity Reductions and New Solutions for the Generalized Variable-Coefficient KdV Equation by Using Symmetry Group Method