Lie group analysis is applied to a mathematical model for thin liquid films, namely a nonlinear fourth order partial differential equation in two independent variables. A three-dimensional Lie symmetry algebra is found and reductions to fourth order ordinary differential equations are obtained by using its one-dimensional subalgebras. Two of these ordinary differential equations are studied by the reduction method and by the Jacobi last multiplier method, and found to be linearizable. Furthermore, the G-equation and.-equation, namely two of the heir-equations obtained by iterating the nonclassical symmetries method, are constructed and reductions to different ordinary differential equations are acquired by using two-dimensional and three-dimensional subalgebras, respectively.
Group analysis and heir-equations of a mathematical model for thin liquid films / S. MARTINI; CICCOLI, Nicola; NUCCI, Maria Clara. - In: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS. - ISSN 1402-9251. - STAMPA. - 16:1(2009), pp. 77-92. [10.1142/S1402925109000078]
Group analysis and heir-equations of a mathematical model for thin liquid films
NUCCI, Maria Clara
2009
Abstract
Lie group analysis is applied to a mathematical model for thin liquid films, namely a nonlinear fourth order partial differential equation in two independent variables. A three-dimensional Lie symmetry algebra is found and reductions to fourth order ordinary differential equations are obtained by using its one-dimensional subalgebras. Two of these ordinary differential equations are studied by the reduction method and by the Jacobi last multiplier method, and found to be linearizable. Furthermore, the G-equation and.-equation, namely two of the heir-equations obtained by iterating the nonclassical symmetries method, are constructed and reductions to different ordinary differential equations are acquired by using two-dimensional and three-dimensional subalgebras, respectively.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.