Similarity solutions of the Konopelchenko–Dubrovsky system using Lie group theory

This research deals with the similarity solutions of (2+12+1)-dimensional Konopelchenko–Dubrovsky (KD) system. Solutions so obtained are derived by using similarity transformations method based on Lie group theory. The method reduces the number of independent variables by one exploiting Lie symmetries and using invariance property. Thus, the KD system can further be reduced to a new system of ordinary differential equations. Under a suitable choice of functions and the arbitrary constants, these new equations yield the explicit solutions of the KD system which are discussed in the Similarity Solutions section of the article. Moreover, the physical analysis of the solutions is illustrated graphically in the Analysis and Discussions section based on numerical simulations in order to highlight the importance of the study.