TY - JOUR
T1 - Conservation laws for one-layer shallow water wave systems
AU - Yaşar, Emrullah
AU - Özer, Teoman
PY - 2010/4
Y1 - 2010/4
N2 - 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. Ibragimov, 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-Bäcklund 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.
AB - 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. Ibragimov, 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-Bäcklund 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.
KW - Conservation laws
KW - Shallow water wave systems
KW - Symmetry groups
UR - http://www.scopus.com/inward/record.url?scp=70449630122&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2009.01.028
DO - 10.1016/j.nonrwa.2009.01.028
M3 - Article
AN - SCOPUS:70449630122
SN - 1468-1218
VL - 11
SP - 838
EP - 848
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
IS - 2
ER -