Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mfenced separators="|"><mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">′</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:mrow></mml:mfenced></mml:mrow></mml:math>-Expansion Method

We apply the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mfenced separators="|"><mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">′</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:mrow></mml:mfenced></mml:mrow></mml:math>-expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigonometric solutions, exponential solutions, and rational solutions. The applications of the method are simple, efficient, and reliable by means of using a symbolically computational package. Applying the proposed method to the problems, we have some innovative exact solutions which are different from the ones obtained using other methods employed previously.