Abstract
In the present study, we have applied similarity transformation method via Lie symmetry approach on the Konopelchenko–Dubrovsky (KD) equation. We have generated infinite-dimensional Lie algebra and commutation relations of the KD equation. The KD equation reduced into a system of ordinary differential equations (ODEs) by employing similarity reductions. Ultimately, the exact solutions of such system of ODEs provided various families of new group-invariant solutions of the KD equation. Furthermore, we have discussed the dynamics of each solution such as multisoliton, doubly solitons, periodic multisoliton, multiple wavefront, solitons interactions, parabolic and stationary wave through their evolution profiles. Numerical simulations have been performed by taking appropriate choices of arbitrary functions and constants involved in the solutions.
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