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Wyświetlanie 1-7 z 7
Tytuł:
Embedded Solitons and Conservation Law with $χ^{(2)}$ and $χ^{(3)}$ Nonlinear Susceptibilities
Autorzy:
Savescu, M.
Kara, A.
Kumar, S.
Krishnan, E.
Zaka Ullah, M.
Moshokoa, S.
Zhou, Qin
Biswas, A.
Powiązania:
https://bibliotekanauki.pl/articles/1398312.pdf
Data publikacji:
2017-02
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
solitons
χ^{(2)}
conservation laws
Opis:
This paper studies embedded solitons that are confined to continuous spectrum, with $χ^{(2)}$ and $χ^{(3)}$ nonlinear susceptibilities. Bright and singular soliton solutions are obtained by the method of undetermined coefficients. Subsequently, the Lie symmetry analysis and mapping method retrieves additional solutions to the model such as shock waves, singular solitons, cnoidal waves, and several others. Finally, a conservation law for this model is secured through the Lie symmetry analysis.
Źródło:
Acta Physica Polonica A; 2017, 131, 2; 297-303
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global existence for strong solutions of viscous Burgers equation. (1) The bounded case
Autorzy:
Unterberger, J.
Powiązania:
https://bibliotekanauki.pl/articles/206077.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
viscous Burgers equation
conservation laws
maximum principle
Schauder estimates
Opis:
We prove that the viscous Burgers equation (∂t−∆)u(t, x)+( u •∇)u(t, x) = g(t, x), (t, x) ∈ R+ × Rd (d ≥ 1) has a globally defined smooth solution in all dimensions provided the initial condition and the forcing term g are smooth and bounded together with their derivatives. Such solutions may have infinite energy. The proofdoes not rely on energy estimates, but on a combinationof the maximumprinciple and quantitative Schauder estimates. We obtain precise bounds on the sup norm of the solution and its derivatives, making it plain that there is no exponential increase in time. In particular, these bounds are time-independent if g is zero. To get a classical solution, it suffices to assume that the initial condition and the forcing term have bounded derivatives up to order two.
Źródło:
Control and Cybernetics; 2017, 46, 2; 109-136
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Conservation Laws in Physics. Emmy Noether’s Theorem
Autorzy:
Manolea, D.
Powiązania:
https://bibliotekanauki.pl/articles/412434.pdf
Data publikacji:
2014
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
practical character of physics
conservation laws
Emmy Noerther’s Theorem
Opis:
The study is explanatory-interpretative and argues the practical character of Physics. It starts from premise that formation of a correct conception of the world begins with the understanding of physics. It is one of the earliest chapters of human knowledge, studying the material world from the microscopic level of the particles to the macroscopic level of the celestial body. As an example for the practical importance of applying the laws of physics take the set of physical laws of conservation, in particular, it explains the practical impact of Emmy Noether's Theorem.
Źródło:
International Letters of Chemistry, Physics and Astronomy; 2014, 10; 55-61
2299-3843
Pojawia się w:
International Letters of Chemistry, Physics and Astronomy
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the numerical discretization of optimal control problems for conservation laws
Autorzy:
Schäfer Aguilar, Paloma
Schmitt, Johann Michael
Ulbrich, Stefan
Moos, Michael
Powiązania:
https://bibliotekanauki.pl/articles/1839148.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
conservation laws
adjoint state
linear transport equation
discontinuous coefficients
finite difference schemes
Opis:
We analyze the convergence of discretization schemes for the adjoint equation arising in the adjoint-based derivative computation for optimal control problems governed by entropy solutions of conservation laws. The difficulties arise from the fact that the correct adjoint state is the reversible solution of a transport equation with discontinuous coefficient and discontinuous end data. We derive the discrete adjoint scheme for monotone difference schemes in conservation form. It is known that convergence of the discrete adjoint can only be expected if the numerical scheme has viscosity of order O(h) with appropriate 0 < α < 1, which leads to quite viscous shock profiles. We show that by a slight modification of the end data of the discrete adjoint scheme, convergence to the correct reversible solution can be obtained also for numerical schemes with viscosity of order O(h) and with sharp shock resolution. The theoretical findings are confirmed by numerical results.
Źródło:
Control and Cybernetics; 2019, 48, 2; 345-376
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Balance errors in numerical solutions of shallow water equations
Autorzy:
Gąsiorowski, D.
Powiązania:
https://bibliotekanauki.pl/articles/1933150.pdf
Data publikacji:
2007
Wydawca:
Politechnika Gdańska
Tematy:
shallow water equations
nonlinear advection equations
numerical errors
conservation laws
mass and momentum balance
Opis:
An analysis of the conservative properties of shallow water equations is presented, focused on the consistency of their numerical solution with the conservation laws of mass and momentum. Two different conservative forms are considered, solved by an implicit box scheme. Theoretical analysis supported with numerical experiments is carried out for a rectangular channel and arbitrarily assumed flow conditions. The improper conservative form of the dynamic equation is shown not to guarantee a correct solution with respect to the conservation of momentum. Consequently, momentum balance errors occur in the numerical solution. These errors occur when artificial diffusion is simultaneously generated by a numerical algorithm.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2007, 11, 4; 329-340
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Isospectral integrability analysis of dynamical systems on discrete manifolds
Autorzy:
Blackmore, D.
Prykarpatsky, A. K.
Prykarpatsky, Y. A.
Powiązania:
https://bibliotekanauki.pl/articles/255384.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
gradient holonomic algorithm
conservation laws
asymptotic analysis
Poissonian structures
Lax representation
finite dimensional reduction
Liouville integrability
nonlinear discrete dynamical systems
Opis:
It is shown how functional-analytic gradient-holonomic structures can be used for an isospectral integrability analysis of nonlinear dynamical systems on discrete manifolds. The approach developed is applied to obtain detailed proofs of the integrability of the discrete nonlinear Schrödinger, Ragnisco-Tu and Riemann-Burgers dynamical systems.
Źródło:
Opuscula Mathematica; 2012, 32, 1; 41-66
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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 1-7 z 7

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