,Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+ 1)-dimensions

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Through the Hirota bilinear formulation and the symbolic computation software Maple,we construct lump-type solutions for a generalized (3+ l)-dimensional Kadomtsev-Petviashvili (KP) equation in three cases of the coefficients in the equation.Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions (or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed.To illustrate the generality of the obtained solutions,two concrete lump-type solutions are explicitly presented,and to analyze the dynamic behaviors of the solutions specifically,the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.
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