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\fancyhead[CO]{\zihao{5}内蒙古工业大学硕士学位论文 }
\fancyhead[CE]{\zihao{5} 内蒙古工业大学硕士学位论文}
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 \centerline{\heiti \zihao{3}摘~~~~~~要}
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自然界存在丰富的非线性现象，这类现象均可归纳为特定非线性问题. 分数阶非线性偏微分方程能精准描述复杂物理过程，已经广泛应用于流体力学、等离子体物理等领域，借助数学解析方法研究该类模型，可清晰揭示系统物理演化机制，为理解自然现象的规律与本质提供支撑. 因其广泛的工程与科学应用价值，分数阶微分方程备受学者关注，其中呼吸子解、孤子解等解析解对应的非线性波研究尤为突出，这类解析解可有效模拟海洋波动、离子声波等复杂的非线性行为.\\

{\noindent \heiti 关键词：}分数阶非线性偏微分方程；KP方程族约化方法；Hirota~方法；呼吸子；孤子

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 \centerline{\bf\Large Abstract}
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 {\rm } Nonlinear phenomena are ubiquitous in nature, and all of them can be generalized into specific nonlinear problems. Nonlinear fractional partial differential equations (FPDEs) are capable of depicting complex physical processes with high precision and have been widely applied in disciplines including fluid mechanics and plasma physics. Adopting mathematical analytical methods to study such models can explicitly reveal the physical evolution mechanisms of relevant systems, thus laying a theoretical foundation for understanding the inherent laws and essences of natural phenomena. Owing to their extensive applicability in engineering and scientific research, fractional differential equations have attracted considerable attention from scholars. Research on nonlinear waves associated with analytical solutions—such as solitons and breather solutions—is particularly prominent, effectively simulating complex nonlinear behaviors like ocean waves and ion acoustic waves.
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{\noindent\bf Key words:}{\sf \rm ~~Nonlinear Fractional partial differential equation; KP hierarchy reduction method; Hirota method; Breather solution; Solitons}
