Melnikov I., Wave Motion 2024 Vol. 130 Article 103380
Non-reflective wave propagation is of great importance for applications because it allows energy to be transmitted over long distances. The paper discusses the method of reducing the equations of the linear theory of shallow water to a wave equation with a variable coefficient in the form of an inverse hyperbolic sine, the solution of which ...
Added: July 10, 2024
Ioann Melnikov, Pelinovsky E., Physics of Fluids 2024 Vol. 36 No. 7 Article 076609
A method for the transformation of linear shallow water equations based on a generalization of the Carrier–Greenspan transform, well known in the theory of wave rolling on a flat slope, is presented. Thanks to it, the initial equations for waves over arbitrary bathymetry are reduced to a wave equation, from which both the displacement of ...
Added: July 9, 2024
Kulagin N. E., L.M. Lerman, Physica D: Nonlinear Phenomena 2023 Vol. 454 Article 133845
We study in this pap er the existence of periodically modulated in one variable and localized in another variable solutions to the cubic Swift-Hohenberg equation on the plane R2. In the first part we try to apply the method by Kirschgassner-Mielke to reduce the problem to the search of finite-dimensional submanifolds with periodic orbits on
them in some formal ...
Added: July 27, 2023
A. E. Rassadin, Agalarov A. M., Ferroelectrics 2021 Vol. 576 No. 1 P. 40–49
Using the Euler-Lagrange dynamics of the Landau-GinzburgDevonshire functional for homogeneous ferroelectric chain in the spatial continuous limit, (1þ 1)D-nonlinear Klein-Gordon-Fock equation has been derived. Elementary four-terminal network of this ferroelectric chain has been considered as a Hamiltonian system corresponding to the point mass in the effective nonlinear potential. Expressing all parameters of automodeling solution of ...
Added: December 8, 2022
Beklaryan A., Advances in Systems Science and Applications 2020 Vol. 20 No. 2 P. 56–70
The article discusses construction of traveling wave type solutions for the Frenkel-Kontorova model on the propagation of longitudinal waves. For the first time, based on the existence and uniqueness theorem of traveling wave type solutions, as well as the approximation theorem, a complete family of traveling wave type solutions is constructed in the form of ...
Added: June 30, 2020
Fehér L., Marshall I., Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics 2019 P. 1217–1262
Integrable many-body systems of Ruijsenaars–Schneider–van Diejen type displaying action-angle duality are derived by Hamiltonian reduction of the Heisenberg double of the Poisson–Lie group SU(2n). New global models of the reduced phase space are described, revealing non-trivial features of the two systems in duality with one another. For example, after establishing that the symplectic vector space ...
Added: March 7, 2019
Beklaryan L. A., Beklaryan A., Gornov A., , in: Optimization and Applications 9th International Conference, OPTIMA 2018, Petrovac, Montenegro, October 1–5, 2018, Revised Selected Papers.: Springer International Publishing, 2019. P. 291–305.
This paper deals with the implementation of numerical methods for searching for traveling waves for Korteweg–de Vries-type equations with time delay. Based upon the group approach, the existence of traveling wave solution and its boundedness are shown for some values of parameters. Meanwhile, solutions constructed with the help of the proposed constructive method essentially extend ...
Added: January 10, 2019
Beklaryan A., Beklaryan L., Gornov A., , in: Book of abstracts of the IX International Conference on Optimization Methods and Applications (OPTIMA-2018), Petrovac, Montenegro, October 1-5, 2018.: M.: [б.и.], 2018. P. 41–41.
This paper deals with the implementation of numerical methods for searching for traveling waves for Korteweg-de Vries-type equations with time delay. Based upon the group approach, the existence of traveling wave solution and its boundedness are shown for some values of parameters. Meanwhile, solutions constructed with the help of the proposed constructive method essentially extend the class of systems, possessing solutions ...
Added: October 9, 2018
Obodan N., Lebedeyev O., Gromov V., NY: Springer Publishing Company, 2013.
The analysis presented of non-axisymmetrically deformed shells behaviour reveals
the variety of shell features affecting not only critical loads but also postbuckling
behaviour and structural workability as well. These features are profoundly con-nected, not with load and structural irregularities, but with properties of nonlinear
solutions inherent to thin shells.
Non-axisymmetric deformation of shells demonstrates significant subcritical
deflections and the possibility ...
Added: October 4, 2018
Beklaryan A., Beklaryan L. A., , in: Proceedings of the VIII International Conference on Optimization and Applications (OPTIMA-2017), Petrovac, Montenegro, October 2-7, 2017.: [б.и.], 2017. P. 81–87.
For equations of mathematical physics, which are the Euler-Lagrange equation of the corresponding variational problem, an important class of solutions are traveling wave solutions (soliton solutions). In turn, soliton solutions for finite-difference analogs of the equations of mathematical physics are in one-to-one correspondence with solutions of induced functional differential equations of pointwise type (FDEPT). The ...
Added: November 14, 2017
Kantonistova E., Фоменко А. Т., Springer, 2015.
Added: October 30, 2017