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ردیف | عنوان | نوع |
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1 |
Conservation laws of the one-dimensional equations of relativistic gas dynamics in Lagrangian coordinates
قوانین حفاظت از معادلات یک بعدی پویایی گاز نسبی در مختصات لاگرانژی-2020 The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The
studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that
the relativistic gas dynamics equations can be rewritten in a variational form. Such a Lagrangian is found in
the paper. Complete group analysis of the Euler–Lagrange equation is performed. The found Lagrangian and
the symmetries are used to derive conservation laws in Lagrangian variables by means of Noether’s theorem.
The analogs of the newly found conservation laws in Eulerian coordinates are presented as well. Keywords: Relativistic gas dynamics | Symmetry | Noether’s theorem | Conservation law |
مقاله انگلیسی |
2 |
Variational symmetries and conservation laws of the wave equation in one space dimension
تقارن های متغیر و قوانین حفاظت از معادله موج در یک بعد فضا-2020 The direct method based on the definition of conserved currents of a system of
differential equations is applied to compute the space of conservation laws of the
(1+1)-dimensional wave equation in the light-cone coordinates. Then Noether’s
theorem yields the space of variational symmetries of the corresponding functional.
The results are also presented for the standard space–time form of the wave
equation. Keywords: Wave equation | Variational symmetry | Conservation law | Noether’s theorem | Direct method |
مقاله انگلیسی |
3 |
Shallow water equations in Lagrangian coordinates: Symmetries, conservation laws and its preservation in difference models
معادلات کم عمق آب در مختصات لاگرانژی: تقارن ، قوانین حفاظت و حفظ آن در اختلاف مدل ها -2020 The one-dimensional shallow water equations in Eulerian and Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in La- grangian (potential) coordinates and symmetries and conservation laws in mass Lagrangian variables. For equations in Lagrangian coordinates with a flat bottom an invariant differ- ence scheme is constructed which possesses all the difference analogues of the conserva- tion laws: mass, momentum, energy, the law of center of mass motion. Some exact invari- ant solutions are constructed for the invariant scheme, while the scheme admits reduction on subgroups as well as the original system of equations. For an arbitrary shape of bottom it is possible to construct an invariant scheme with conservation of mass and momentum or, alternatively, mass and energy.. Invariant conservative difference scheme for the case of a flat bottom tested numerically in comparison with other known schemes. Keywords: Shallow water | Lagrangian coordinates | Lie point symmetries | Conservation law | Noether’s theorem | Numerical scheme |
مقاله انگلیسی |