Pattern Transformation in Higher-Order Lumps of the Kadomtsev–Petviashvili I Equation
Pattern Transformation in Higher-Order Lumps of the Kadomtsev–Petviashvili I Equation
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DOI：
10.1007/s00332-022-09807-8
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发表时间：
2021-10
影响因子：
3
通讯作者：
Bo Yang;Jianke Yang
中科院分区：
文献类型：
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作者：
Bo Yang;Jianke Yang
本文对Kadomtsev-Petviashvili方程高阶块在大时间内的模式形成进行了分析研究。对于这些高阶块的广泛类别，我们证明了两种类型的解模式在大时间出现。第一种模式包括以三角形排列的基本块，它们由Yablonskii-Vorob 'ev多项式的根结构解析描述。随着时间从大的负值演变为大的正值，这个三角形图案沿着x方向反转。第二种模式包括在外部区域以非三角形形状排列的基本团块，它们由wronskii - hermit多项式的非零根结构解析描述，以及在内部区域以三角形形状排列的可能的基本团块，它们由Yablonskii-Vorob 'ev多项式的根结构解析描述。当时间从大负向大正演变时，外部区域的非三角形图案会改变其方向，而内部区域的三角形图案如果出现，则会沿着六轴方向反转。我们的预测模式在大时间内与真实的解决方案进行比较，并观察到极好的一致性。
Pattern formation in higher-order lumps of the Kadomtsev–Petviashvili I equation at large time is analytically studied. For a broad class of these higher-order lumps, we show that two types of solution patterns appear at large time. The first type of patterns comprises fundamental lumps arranged in triangular shapes, which are described analytically by root structures of the Yablonskii–Vorob’ev polynomials. As time evolves from large negative to large positive, this triangular pattern reverses itself along thex-direction. The second type of patterns comprise fundamental lumps arranged in non-triangular shapes in the outer region, which are described analytically by nonzero-root structures of the Wronskian–Hermit polynomials, together with possible fundamental lumps arranged in triangular shapes in the inner region, which are described analytically by root structures of the Yablonskii–Vorob’ev polynomials. When time evolves from large negative to large positive, the non-triangular pattern in the outer region switches itsxandydirections, while the triangular pattern in the inner region, if it arises, reverses its direction along thex-axis. Our predicted patterns at large time are compared to true solutions, and excellent agreement is observed.