Temat: KdV equation - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach
Autorzy:: Klamka, Jerzy
Avetisyan, Ara S.
Khurshudyan, Asatur Zh.
Powiązania:: https://bibliotekanauki.pl/articles/229650.pdf
Data publikacji:: 2020
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: KdV equation
Boussinesq equation
Frasca’s method
short time expansion
traveling wave
heuristic method
distributed control
constrained controllability
Opis:: In this paper, we study the constrained exact and approximate controllability of traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green’s function approach. Control is carried out by a moving external source. Representing the general solution of those equations in terms of the Frasca’s short time expansion, system of constraints on the distributed control is derived for both types of controllability. Due to the possibility of explicit solution provided by the heuristic method, the controllability analysis becomes straightforward. Numerical analysis confirms theoretical derivations.
Źródło:: Archives of Control Sciences; 2020, 30, 1; 177-193
1230-2384
Pojawia się w:: Archives of Control Sciences
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 2.

Tytuł:: Exact Cnoidal Solutions of the Extended KdV Equation
Autorzy:: Infeld, E.
Karczewska, A.
Rowlands, G.
Rozmej, P.
Powiązania:: https://bibliotekanauki.pl/articles/1030809.pdf
Data publikacji:: 2018-05
Wydawca:: Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:: shallow water waves
extended KdV equation
analytic solutions
inverted cnoidal waves
Opis:: The KdV equation can be derived within the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include both higher order effects (KdV2) and an uneven river bottom. Although this equation is not integrable and has only one conservation law, exact periodic and solitonic solutions exist for the even bottom case. The method used to find them assumes the same functional forms as for KdV solutions. The KdV2 equation imposes more constraints on the parameters of solutions. Quite unexpectedly, we found two regions in m parameter space for periodic solutions. For the range of m close to one the cnoidal waves are upright as expected, but are inverted in the m region close to zero which is a completely new feature. The properties of exact solutions for KdV and KdV2 are compared. Numerical evolution of all the discussed exact solutions to KdV2 is stable and confirms the properties of the analytic solutions.
Źródło:: Acta Physica Polonica A; 2018, 133, 5; 1191-1199
0587-4246
1898-794X
Pojawia się w:: Acta Physica Polonica A
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Informacja

Wyszukujesz frazę "KdV equation" wg kryterium: Temat

Źródło danych

Dostawca treści

Kolekcja

Rok wydania

Wydawca

Temat

Autor

Typ dokumentu

Język