Pattern Transformation in Higher-Order Lumps of the Kadomtsev–Petviashvili I Equation

Pattern formation in higher-order lumps of the Kadomtsev–Petviashvili I equation at large time is analytically studied. For a broad class these lumps, we show that two types solution patterns appear time. The first type comprises fundamental arranged triangular shapes, which are described by root structures Yablonskii–Vorob’ev polynomials. As evolves from negative to positive, this pattern reverses itself along x-direction. second comprise non-triangular shapes outer region, nonzero-root Wronskian–Hermit polynomials, together with possible inner When region switches its x and y directions, while if it arises, direction x-axis. Our predicted compared true solutions, excellent agreement observed.