Nonlinear dynamical analysis to explore the N-soliton solutions of time-fractional coupled Burger’s model

Abstract

The modeling of nonlinear dynamical models and their solutions have imperative values, whereas the soliton mathematical methods are favorable tools for analyzing such highly nonlinear practical problems. Herein, time-fractional coupled Burger’s model is analyzed. Some solitary wave solutions, containing one-soliton, two-soliton, three-soliton and [Formula: see text]-soliton, have been fetched using a modified sort of the well-known exp-function approach. Dominant effects of the fractional parameters have been illustrated and it is noted that the higher values of the fractional number cause a significant impact on the wave propagation. The one wave pattern for the [Formula: see text]-component is quite identical, while an increase in the fractional parameter is producing an increment in the wave structure while a similar but opposite pattern is noted for the [Formula: see text]-component. An increment in the wave structure is noted for higher values of the time-fractional parameter for both [Formula: see text]- and [Formula: see text]-components in the case of a two-wave solution. The benefits of the proposed computational code of the exp-function scheme are consistent, a general form of exact solutions, reduced computational complexity and stable and efficiently useful. The obtained solitary waves solutions will be a useful extension to the preceding results and greatly assist in clarifying the features of nonlinear waves in viscous flow.