Rosenau and Hyman introduced compactons as a solution of the K(m, n) equation which generalizes the celebrated Korteweg-De Vries (KdV) equation. The inclusion of the generalized K (𝑓 m , g n ) equation as a central part of the Kadomtsev-Petviashvili (KP) equation results in a generalized KP-like equationIn this article, we present the general form of conservation laws for the nonlinear KP (𝑓 m , g n ) equation, in terms of unknown functions 𝑓 and g, by employing the multipliers approach. For suitable choices of m, n, 𝑓 , and g, the derived conservation laws are utilized to obtain conservation laws for several variants of the KP equation, including the logarithmic KP-like equation, the generalized Gardner KP equation, and the KP equation with p-power non-linearity.The double reduction theory is employed to construct reductions and exact solutions of various KP-like generalized equations, including the KP (u m , u n ) equation for different values of m and n. The structure of these solutions is analyzed by some graphs that illustrate soliton and compacton solutions for different parameter values.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.