A Numerical Method for Constructing Attractors of Evolutionary Filtration Equations

Salnikov, A. M.; Akhmetzianov, Atlas V.; Kushner, Alexei G.; Lychagin, Valentin

doi:10.1109/summa48161.2019.8947585

Cited by 5 publications

(1 citation statement)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A method for constructing attractors for second-order evolutionary differential equations was proposed in [1], on the basis of which an algorithm for the numerical solution of such equations was developed in [6].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and exact solutions of the generalized Harry Dym equation

Matviichuk

2020

PIGC

View full text Add to dashboard Cite

The Harry Dym equation is the third-order evolutionary partial differential equation. It describes a system in which dispersion and nonlinearity are coupled together. It is a completely integrable nonlinear evolution equation that may be solved by means of the inverse scattering transform. It has an infinite number of conservation laws and does not have the Painleve property. The Harry Dym equation has strong links to the Korteweg – de Vries equation and it also has many properties of soliton solutions. A connection was established between this equation and the hierarchies of the Kadomtsev – Petviashvili equation. The Harry Dym equation has applications in acoustics: with its help, finite-gap densities of the acoustic operator are constructed. The paper considers a generalization of the Harry Dym equation, for the study of which the methods of the theory of finite-dimensional dynamics are applied. The theory of finite-dimensional dynamics is a natural development of the theory of dynamical systems. Dynamics make it possible to find families that depends on a finite number of parameters among all solutions of evolutionary differential equations. In our case, this approach allows us to obtain some classes of exact solutions of the generalized equation, and also indicates a method for numerically constructing solutions.

show abstract

Section: Introductionmentioning

confidence: 99%