General Expa-function method for nonlinear evolution equations

This work generalizes the exponential function method in considering an arbitrary base “a” as opposed to the conventional base “e” for the exponential function. The combined KdV-mKdV equation is considered to reveal the effectiveness and convenience of the proposed generalization. The study highlights the power of the proposed method on constructing solutions expressed in terms of exponential, hyperbolic, periodic, symmetrical Fibonacci, symmetrical Lucas, and k-Fibonacci functions. Some of the obtained solitary wave solutions are sketched graphically.