The dynamical behavior for a famous class of evolution equations with double exponential nonlinearities

Abstract

An analytical investigation for a famous class of evolution equations with double exponential nonlinearities that has vast applications in many nonlinear sciences is presented. These equations include the Tzitzéica Equation (TE), Dodd-Bullough-Mikhailov Equation (DBME), Tzitzéica-Dodd-Bullough-Mikhailov equation (TDBME) and the Peyrard Bishop DNA Equation (PB-DNA-E). Furthermore, the Kudryashov method for constructing exponential function solutions has been employed to reveal various sets of traveling wave solutions with different geometrical structures to the identified models. We also give the graphical illustrations of certain solutions to further analyze the results.