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A Weierstrass type projective Riccati equation expansion method is proposedby using the Weierstrass elliptic function solutions of the projective Riccatiequations and the conversion formulas which transform the Weierstrass ellipticfunctions into the hyperbolic and the trigonometric functions. The Weierstrasselliptic function solutions and their degenerated solutions including thesolitary wave and the periodic wave solutions of the mKdV equation are obtainedby using the proposed method.

A method for constructing Weierstrass elliptic function solutions and their degenerated solutions of the mKdV equation