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International School “Singularities, Blow-up, and Non-Classical
Problems in Nonlinear PDEs for youth”
13 ноября 2024 г. 13:30–14:30, г. Москва, РУДН
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Traveling wave solutions to nonlinear wave equations: dynamical system approach. Lecture 1
Lijun Zhang Zhejiang University of Science and Technology, China
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Аннотация:
The dynamical system approach has been well applied to study the traveling wave
solutions of various nonlinear wave equations in recent two decades. In this talk, the main
ideal and the key steps of this approach to investigate the traveling wave solutions of
nonlinear wave equations will be introduced firstly. In addition to the exact solutions, the
bifurcations of the traveling wave solutions and various smooth or non-smooth can be
derived via this approach. The advantage and the challenging of this method is discussed
as well. How this approach is extended to examine the traveling waves solutions, even the
multi-wave solutions of higher-order nonlinear wave equations will be presented. Some
recent development and works on the persistence of traveling wave solutions and the new
solitary wave solutions to some classical nonlinear wave equations under singular
perturbation via combining the singular perturbation method and bifurcation analysis are
presented.
Язык доклада: английский
Цикл лекций
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