Elements of the theory of solitons

2025/2026

Учебный год

ENG

Обучение ведется на английском языке

Кто читает:

Кафедра фундаментальной математики (Факультет информатики, математики и компьютерных наук (Нижний Новгород))

Статус:

Курс обязательный

Когда читается:

1-й курс, 3, 4 модуль

Преподаватели

Диденкулова Екатерина Геннадьевна

Слюняев Алексей Викторович

Course Syllabus

Abstract

Solitons – structurally stable wave objects in nonlinear dynamical systems — were discovered in the 1970s in a series of basic nonlinear equations of physics; the class of soliton-like solutions of integrable and non-integrable equations continues to broaden. Solitons are essential or even dominant parts of wave solutions in practically important problems of physics (for example, the data transmission by optical pulses, internal waves and rogue waves in the ocean, non-destructive diagnostics of composite materials) and much beyond. The elaboration of the theory of solitons and of the theory of integrable systems has yielded the appearance and ongoing development of the corresponding mathematical techniques, and also broadening of the field of practical applications. The course will give an introduction to the theory of solitons – as a part of nonlinear dynamics. The distinctive features of these structures among nonlinear waves, the variety of their manifestations (solitons, envelope solitons, breathers) will be shown. The key elements of the Inverse Scattering Technique, and also the basic examples will be discussed. On the basis of multisoliton solutions, the features of the nonlinear wave interaction and focusing will be considered. Actual problems of the scientific research in the fields of nonlinear optics and hydrodynamics will be emphasized.