On the localized travelling wave solutions to some non-linear evolution PDEs, obtained within the modified algebraic method

Abstract:
We present some modification of the ansatz-based method, used for obtaining exact solutions to the non-linear PDEs. The modified ansatz-based method is used in this work for finding solutions with the given properties (periodic, kink-like and soliton-like solutions) of the non-linear telegraph equation, non-linear d'Alembert equation, hyperbolic modification of the Burgers equation and two-component system of PDEs, related to  a mathematical model of somitogenesis.