Dynamics of mixed lump-solitary waves of an extended (2 + 1)-dimensional shallow water wave model

To explore the features of lump solutions, which are local in every direction of space, a (2+1)-dimensional extended shallow water wave model is studied, based on its bilinear representation. Several ansatzes have been utilized to determine single lump waves, lump-kink waves, single kinks and multi-lumps leading to breathers in terms of function patterns for the model. Through analyzing interactions between solitons, the impact of free parameters involved in the solutions on interaction types is exhibited. We determine a condition on the parameters under which a single kink wave can be converted into a multi-lump wave. To illustrate the interaction of exponential and periodic function waves, we show that multi-lump waves in the form of breather waves especially come into sight as a straight line or an X shape. To realize dynamics, we make various graphical analyses on the presented solutions, which gives an essential improvement in the physical realizing of higher-dimensional lump waves in oceanography and nonlinear optics.