Fifth-order evolution equation for a liquid film with odd viscosity

A fifth-order nonlinear wave equation (generalized Korteweg–deVries equation) that arises in the theory of thin liquid films is introduced with the odd viscosity by the long-wave approximation regime. The presence of the odd viscosity is considered to be a non-dissipative factor in the evolution of the film flow. Sinusoidal and travelling waves arise in systems with non dissipation and instability. The introduced wave equation includes quadratic and cubic nonlinearities. The linear instability of sinusoidal waves is analyzed. The stability and bifurcation of travelling waves are discussed.