Abstract
The Kadomtsev–Petviashvili equation and its variants play a significant role in the description of several nonlinear phenomena arising in physics. In this paper, a new extension of the Kadomtsev–Petviashvili equation is considered. The main objective of this work is to study the traveling wave dynamics of the considered equation. Different traveling patterns are obtained for the governing equation in the presented work. Traveling wave solutions involving solitonic structures are derived by the application of the modified auxiliary equation method. The proposed method has provided solutions involving trigonometric, hyperbolic and rational functions. The wave profiles plotted for the obtained exact solutions exhibit the dark and bright solitons. Moreover, one line rogue wave and breather wave solutions are constructed for the governing model using combination of trigonometric and exponential functions as test functions. The dynamical characteristics of the earned solutions are depicted using interesting plots for deep understanding of obtained results.
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