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http://hdl.handle.net/11452/23261| Title: | Conservation laws for one-layer shallow water wave systems |
| Authors: | Özer, Teoman Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü. 0000-0003-4732-5753 Yaşar, Emrullah AAG-9947-2021 23471031300 |
| Keywords: | Conservation laws Symmetry groups Shallow water wave systems Partial-differential equations Invariant solutions Symmetries Mathematics Barium Differential equations Euler equations Fluorine containing polymers Hydrodynamics Lagrange multipliers Quantum theory Variational techniques Water analysis Water waves Waves Adjoint equations Adjoint variables Axisymmetric flow Conservation law Conservation theorem Dispersive waves Euler-lagrange equations Lagrangian system Local conservation Mathematical analysis Nonlocal Nonlocal variables Plane flow Potential symmetry Shallow water waves Symmetry groups Variational functional Variational principles Wave equations |
| Issue Date: | Apr-2010 |
| Publisher: | Pergamon-Elsevier Science |
| Citation: | Yaşar, E. ve Özer, T. (2010). "Conservation laws for one-layer shallow water wave systems". Nonlinear Analysis-Real World Applications, 11(2), 838-848. |
| Abstract: | The problem of correspondence between symmetries and conservation laws for one-layer shallow water wave systems in the plane flow, axisymmetric flow and dispersive waves is investigated from the composite variational principle of view in the development of the study [N.H. lbragimov, A new conservation theorem, journal of Mathematical Analysis and Applications, 333(1) (2007) 311-328]. This method is devoted to construction of conservation laws of non-Lagrangian systems. Composite principle means that in addition to original variables of a given system, one should introduce a set of adjoint variables in order to obtain a system of Euler-Lagrange equations for some variational functional. After studying Lie point and Lie-Backlund symmetries, we obtain new local and nonlocal conservation laws. Nonlocal conservation laws comprise nonlocal variables defined by the adjoint equations to shallow water wave systems. In particular, we obtain infinite local conservation laws and potential symmetries for the plane flow case. |
| URI: | https://doi.org/10.1016/j.nonrwa.2009.01.028 https://www.sciencedirect.com/science/article/pii/S1468121809000303 http://hdl.handle.net/11452/23261 |
| ISSN: | 1468-1218 |
| Appears in Collections: | Scopus Web of Science |
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