Abstract
By modifying the extended mapping method, we get traveling wave solutions of nonlinear complex physical models, arising in various fields of applied sciences. This method is applied to the (1 + 1)-dimensional Hirota equation. Consequently, different kinds of family of exact traveling wave solutions are fruitfully surveyed. The obtained novel exact traveling wave solutions represent in different forms such as bright and dark solitary wave, periodic solitary wave and dark and bright soliton. These solutions are represented in the form of trigonometric, hyperbolic, exponential and rational functions. The properties of some of the novel traveling wave solutions are shown in figures. The obtained results exhibit the effectiveness, power and exactness of the method that can be used for many other nonlinear problems.