Exact solutions to nonlinear delay differential equations of hyperbolic type

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

物理学;数学

Vyazmin, Andrei V.^1 ; Sorokin, Vsevolod G.^2,3

Moscow State University of Mechanical Engineering, 38 Bolshaya Semenovskaya Street, Moscow

107023, Russia^1

Institute for Problems in Mechanics, Russian Academy of Sciences, 101 Vernadsky Avenue, bldg 1, Moscow

119526, Russia^2

Bauman Moscow State Technical University, 5 Second Baumanskaya Street, Moscow

105005, Russia^3

关键词: Approximate analytical methods;    Delay equations;    Differential-difference equations;    Exact solution;    Nonlinear delay differential equation;    Nonlinear differential-difference equation;    Reaction diffusion equations;    Transfer coefficient;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/788/1/012037/pdf
DOI  :  10.1088/1742-6596/788/1/012037

来源: IOP

【 摘 要 】

We consider nonlinear delay differential equations of hyperbolic type, including equations with varying transfer coefficients and varying delays. The equations contain one or two arbitrary functions of a single argument. We present new classes of exact generalized and functional separable solutions. All the solutions involve free parameters and can be suitable for solving certain model problems as well as testing numerical and approximate analytical methods for similar and more complex nonlinear differential-difference equations.