通气管
畸形波
可积系统
非线性系统
等级制度
裂变
物理
双线性插值
复杂系统
经典力学
数学
数学物理
量子力学
计算机科学
中子
法学
统计
人工智能
政治学
作者
Yulei Cao,Yi Cheng,Jingsong He
摘要
Exploring new nonlinear wave solutions to integrable systems has always been an open issue in physics, applied mathematics, and engineering. In this paper, the Maccari system, a two-dimensional analog of nonlinear Schrödinger equation, is investigated. The system is derived from the Kadomtsev–Petviashvili (KP) equation and is widely used in nonlinear optics, plasma physics, and water waves. A large family of semi-rational solutions of the Maccari system are proposed with the KP hierarchy reduction method and Hirota bilinear method. These semi-rational solutions reduce to the breathers of elastic collision and resonant collision under special parameters. In case of resonant collisions between breathers and rational waves, these semi-rational solutions describe lumps fusion into breathers, or lumps fission from breathers, or a mixture of these fusion and fission. The resonant collisions of semi-rational solutions are semi-localized in time (i.e., lumps exist only when t → +∞ or t → −∞), and we also discuss their dynamics and asymptotic behaviors.
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