Waves rogue hai chiều được định vị kép trong phương trình Davey–Stewartson I

Journal of Nonlinear Science - Tập 31 - Trang 1-44 - 2021
Jiguang Rao1,2, Athanassios S. Fokas3, Jingsong He1
1Institute for Advanced Study, Shenzhen University, Shenzhen, People’s Republic of China
2Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen, People’s Republic of China
3DAMTP, University of Cambridge, Cambridge, UK

Tóm tắt

Các sóng rogue hai chiều được định vị kép cho phương trình Davey–Stewartson I trong nền tảng của các soliton tối hoặc một hằng số được nghiên cứu bằng cách sử dụng phương pháp giảm bậc Kadomtsev–Petviashvili kết hợp với kỹ thuật bilinear của Hirota. Những sóng rogue hai chiều này, được mô tả bởi các nghiệm kiểu bán hợp lý, minh họa cho các va chạm cộng hưởng giữa các cục hoặc sóng rogue theo đường thẳng và các soliton tối. Do các va chạm cộng hưởng, các sóng rogue theo đường thẳng và các cục trong những nghiệm bán hợp lý này trở nên được định vị kép trong không gian hai chiều và theo thời gian. Do đó, chúng được gọi là sóng rogue theo đoạn thẳng hoặc sóng rogue kiểu cục. Các sóng này xuất hiện từ nền tảng của các soliton tối, sau đó tồn tại trong nền tảng của các soliton tối trong một khoảng thời gian rất ngắn, và cuối cùng hoàn toàn biến mất trở lại nền tảng của các soliton tối. Trong các trường hợp nhất định được đặc trưng bởi các điều kiện tham số đặc biệt, các soliton tối trong thành phần sóng dài của phương trình DSI có thể suy biến thành nền tảng hằng số. Trong trường hợp này, các sóng rogue xuất hiện và biến mất trong một nền tảng hằng số.

Từ khóa

#sóng rogue #soliton tối #phương trình Davey–Stewartson #phương pháp Kadomtsev–Petviashvili #kỹ thuật bilinear Hirota #va chạm cộng hưởng

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