摘要
本文首先利用拟行列式的性质获得了非交换非等谱Kadomtsev-Petviashvili方程的拟行列式解。作为特例我们研究了一个2×2矩阵环上的非等谱Kadomtsev-Petviashvili方程,分析了解的非等谱特征和耦合作用。由于方程对应于与时间相关的谱参数,由解所描述的孤立波(线孤子)的振幅和传播速度均与时间有关。本文还利用反散射变换获得了非等谱Kadomtsev-Petviashvili 1方程的N-lump解,并分析了解的动力学行为。由于与时间相关的谱参数的影响,不仅可以产生静态的lump波,而且解所提供的lump波在时间上也具有局部性,体现出rouge波的特点。论文对高维非等谱模型的研究和应用提供了可能的背景和基础。。
In the dissertation,we first study a noncommutative nonisospectral Kadomtsev-Petviashvili equation. By means of quasideterminant;we derive exact solutions for the noncommutative nonisospectral Kadomtsev-Petviashvili equation through direct verifica-tion. The obtained solutions are expressed in terms of quasidetcrminants. The solutions behavior like line solitons with time-varying amplitudes and velocities, which coincides with nonisospectral properties resulted from time-dependent spectral parameter. Be-sides, we investigate a nonisospectral Kadomtsev-Petviashvili I equation. We derive its N-lump solutions by means of Inverse Scattering Transform procedure, and investigate nonisospectral dynamics of obtained solutions. Since the spectral parameter of the equa-tion is time-dependent, solutions can provide stationary lump waves which arc localized both spatially and temporally. Such solutions behavior like rogue waves. The study of the dissertation is helpful to understanding backgrounds and possible applications of high dimensional integrablc systems.
引文
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