Control of coupled localized nonlinear wave solutions

5th International Conference on "Problems of Mathematical and Theoretical Physics and Mathematical Modelling"

物理学;数学

Porubov, A.V.^1,2,3 ; Antonov, I.D.^3

Institute of Problems in Mechanical Engineering, Bolshoy 61, V.O., Saint Petersburg

199178, Russia^1

St. Petersburg State University, 7-9, Universitetskaya Nab., V.O., Saint Petersburg

199034, Russia^2

St. Petersburg State Polytechnical University, Polytechnicheskaya st. 29, Saint Petersburg

195251, Russia^3

关键词: Control functions;    Coupled equation;    Initial conditions;    Non-linear dynamics;    Nonlinear waves;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/788/1/012029/pdf
DOI  :  10.1088/1742-6596/788/1/012029

来源: IOP

【 摘 要 】

A method of forced localization of non-linear wave by a feedback control is developed for coupled equations accounting for non-linear dynamic processes in complex lattices. It is shown, that the control of the shape and velocity of the wave function of macro-strain allows to achieve localization of the shape of the function describing variations of defects in the lattice. Moreover, change of the sign of the amplitude of the last wave may be achieved by variation of the parameters of the control function but independent of the initial conditions.