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This paper aims to study a generalized extended (2 + 1) -dimensional Kadomstev–Petviashvili (KP) equation. The KP equation models several physical phenomena such as shallow water waves with weakly nonlinear restoring forces. We will use a variety of wave ansatz methods so as to extract bright, singular, shock waves also referred to as dark or topological or kink soliton solutions. In addition to soliton solutions, we will also derive periodic wave solutions and other analytical solutions based on the invariance surface condition. Moreover, we will establish the multiplier method to derive low-order conservation laws. In order to have a better understanding of the results, graphical structures of the derived solutions will be discussed in detail based on some selected appropriate parametric values in 2-dimensions, 3-dimensions and contour plots. The findings can well mimic complex waves and their underlying properties in fluids. [ABSTRACT FROM AUTHOR]

Kudryashov and Sinelshchikov proposed a nonlinear evolution equation that models the pressure waves in a mixture of liquid and gas bubbles by taking into account the viscosity of the liquid and the heat transfer. Conservation laws and exact solutions are computed for this underlying equation. In the analysis of this particular equation, two approaches are employed, namely, the multiplier method and Kudryashov method. [ABSTRACT FROM AUTHOR]

We compute the conservation laws for the Rosenau-Kortweg de Vries equation coupling with the Regularized Long-Wave equation using Noether's approach through a remarkable method of increasing the order of the Rosenau-KdV-RLW equation. Furthermore, exact solutions for the Rosenau- KdV-RLW equation are acquired by employing the Kudryashov method. [ABSTRACT FROM AUTHOR]