We study the symmetries,conservation laws and reduction of third-order equations that evolve from a prior reduction of models that arise in fluid phenomena.These could be the ordinary differential equations (ODEs)that...We study the symmetries,conservation laws and reduction of third-order equations that evolve from a prior reduction of models that arise in fluid phenomena.These could be the ordinary differential equations (ODEs)that are reductions of partial differential equations (PDEs) or,alternatively,PDEs related to given ODEs.In this class,the analysis includes the well-known Blasius,Chazy,and other associated third-order ODEs.展开更多
A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conse...A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.展开更多
In this work, we study the similarity analysis of the generalized nonlinear Burgers＇ equation having diffusivity and viscosity as a general functions of the particle velocity. We perform the symmetry analysis and exh...In this work, we study the similarity analysis of the generalized nonlinear Burgers＇ equation having diffusivity and viscosity as a general functions of the particle velocity. We perform the symmetry analysis and exhibit exact solutions for various forms of the diffusivity and viscosity.展开更多
文摘We study the symmetries,conservation laws and reduction of third-order equations that evolve from a prior reduction of models that arise in fluid phenomena.These could be the ordinary differential equations (ODEs)that are reductions of partial differential equations (PDEs) or,alternatively,PDEs related to given ODEs.In this class,the analysis includes the well-known Blasius,Chazy,and other associated third-order ODEs.
文摘A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.
文摘In this work, we study the similarity analysis of the generalized nonlinear Burgers＇ equation having diffusivity and viscosity as a general functions of the particle velocity. We perform the symmetry analysis and exhibit exact solutions for various forms of the diffusivity and viscosity.
