We give an introduction to a new direct computational method for constructing multiple soliton solutions to nonlinear equations with variable coefficients in the Kadomtsev-Petviashvili (KP) hierarchy. We discuss in detail how this works for a generalized (3 + 1)-dimensional KP equation with variable coefficients. Explicit soliton, multiple soliton and singular multiple soliton solutions of the equation are obtained under certain constraints on the coefficient functions. Furthermore, the characteristic-line method is applied to discuss the solitonic propagation and collision under the effect of variable coefficients.
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