In this manuscript, we first perform a complete Lie symmetry classification\nfor a higher-dimensional shallow water wave equation and then construct the\ncorresponding reduced equations with the obtained Lie symmetries. Moreover,\nwith the extended F-expansion method, we obtain several new nonlinear\nwave solutions involving differentiable arbitrary functions, expressed by Jacobi\nelliptic function, Weierstrass elliptic function, hyperbolic function and\ntrigonometric function.
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