Complex Wave Solutions to Mathematical Biology Models I: Newell–Whitehead–Segel and Zeldovich Equations

Complex and real valued exact solutions to some reaction-diffusion equations are suggested by using homogeneous balance and Sine-Gordon equation expansion method. The predicted solution of finite series of some hyperbolic functions is determined by using some relations between the hyperbolic functions and the trigonometric functions based on Sine-Gordon equation and traveling wave transform. The Newel–Whitehead–Segel (NWSE) and Zeldovich equations (ZE) are solved explicitly. Some complex valued solutions are depicted in real and imaginary components for some particular choice of parameters.