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    Wyświetlanie 1-6 z 6
    Tytuł:
    When the supersymmetry is not enough; the parasupersymmetric algebras of the Boussines equations
    Autorzy:
    Yourova, A. A.
    Yourov, A. V.
    Yourov, V. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1938588.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Gdańska
    Tematy:
    supersymmetry
    Boussinesq equation
    parasupersymetric
    Opis:
    In this article we look at a conundrum that the Boussinesq-type equations pose for mathematicians allowing a Miura-type transformation while at the same time exhibiting no trace of a supersymmetric structure. We demonstrate that this riddle should be unraveled by dropping the standard supersymmetric approach in favor of its generalization: the “parasupersymmetry”.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2016, 20, 2; 241-248
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dynamics of Shallow Water Waves with Various Boussinesq Equations
    Autorzy:
    Kumar, H.
    Malik, A.
    Singh Gautam, M.
    Chand, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/1033427.pdf
    Data publikacji:
    2017-02
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    Solitons
    exact solutions
    Boussinesq equation
    Opis:
    Attempt has been made to construct the solitary waves and shock wave solutions or domain walls (in higher dimension) for various Boussinesq equations. The method of undetermined coefficients have been used to explore the exact analytical solitary waves and shock wave solutions in terms of bell-shaped sech^p function and kink-shaped tanh^p function for the considered equations. The Boussinesq equation in the (1+1)-dimensional, the (2+1)-dimensional and the (3+1)-dimensional equations are studied and the parametric constraint conditions and uniqueness in view of both solitary waves and shock wave solutions are determined. Such solutions can be valuable and desirable for explaining some nonlinear physical phenomena in nonlinear science described by the Boussinesq equations. The effect of the varying parameters on the development of solitary waves and shock wave solutions have been demonstrated by direct numerical simulation technique.
    Źródło:
    Acta Physica Polonica A; 2017, 131, 2; 275-282
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Rigorous Numerics for PDEs with Indefinite Tail: Existence of a Periodic Solution of the Boussinesq Equation with Time-dependent Forcing
    Autorzy:
    Czechowski, Aleksander
    Zgliczyński, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/1373703.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
    Tematy:
    Boussinesq equation
    ill-posed PDEs
    periodic solutions
    isolating segments
    Opis:
    We consider the Boussinesq PDE perturbed by a time-dependent forcing. Even though there is no smoothing effect for arbitrary smooth initial data, we are able to apply the method of self-consistent bounds to deduce the existence of smooth classical periodic solutions in the vicinity of 0. The proof is non-perturbative and relies on construction of periodic isolating segments in the Galerkin projections.
    Źródło:
    Schedae Informaticae; 2015, 24; 143-158
    0860-0295
    2083-8476
    Pojawia się w:
    Schedae Informaticae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new form of Boussinesq equations for long waves in water of non-uniform depth
    Autorzy:
    Szmidt, J.
    Hedzielski, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/201637.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    long wave
    Boussinesq equation
    wave transformation
    variable water depth
    Opis:
    The paper describes the non-linear transformation of long waves in shallow water of variable depth. Governing equations of the problem are derived under the assumption that the non-viscous fluid is incompressible and the fluid flow is a rotation free. A new form of Boussinesq-type equations is derived employing a power series expansion of the fluid velocity components with respect to the water depth. These non-linear partial differential equations correspond to the conservation of mass and momentum. In order to find the dispersion characteristic of the description, a linear approximation of these equations is derived. A second order approximation of the governing equations is applied to study a time dependent transformation of waves in a rectangular basin of water of variable depth. Such a case corresponds to a spatially periodic problem of sea waves approaching a near-shore zone. In order to overcome difficulties in integrating these equations, the finite difference method is applied to transform them into a set of non-linear ordinary differential equations with respect to the time variable. This final set of these equations is integrated numerically by employing the fourth order Runge - Kutta method.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 3; 631-643
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Tytuł:
    Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions
    Autorzy:
    Kindybaliuk, A.
    Prytula, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/122896.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    nonlinear dynamical system
    conservation laws
    implectic operators
    method of undetermined coefficients
    differential algebraic algorithm
    combined algorithm
    finite dimensional reduction
    Hamiltonian system
    exact solutions
    Boussinesq-Burgers equation
    nieliniowy układ dynamiczny
    prawa zachowania
    algebraiczny algorytm różniczkowy
    system Hamiltona
    rozwiązania dokładne
    równanie Boussinesqa-Burgersa
    Opis:
    In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 3; 85-99
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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