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Equivalent Lagrangians and the Inverse Variational Problem with Applications
Abstract
We show how
the study of the invariance of the functional in the variational
problem is used for the construction of Lagrangians
for some target equations from equations whose Lagrangians are known. Where the
Lagrangian is not unique, we have the freedom to choose the Lagrangian
that is most suitable (for e.g., one that admits the maximal Noether algebra
of point symmetry generators). The method may be used in the multi dimensional
case in the dependent and independent variables. A
variety of examples with discussions are presented.
Mathematics Subject Classification
(2000): 34A55, 35A15, 76M60.
Key
words: Equivalent Lagrangians, symmetry methods.
Quaestiones Mathematicae 27(2004), 207-216.
the study of the invariance of the functional in the variational
problem is used for the construction of Lagrangians
for some target equations from equations whose Lagrangians are known. Where the
Lagrangian is not unique, we have the freedom to choose the Lagrangian
that is most suitable (for e.g., one that admits the maximal Noether algebra
of point symmetry generators). The method may be used in the multi dimensional
case in the dependent and independent variables. A
variety of examples with discussions are presented.
Mathematics Subject Classification
(2000): 34A55, 35A15, 76M60.
Key
words: Equivalent Lagrangians, symmetry methods.
Quaestiones Mathematicae 27(2004), 207-216.
