Abstract

An asymptotic longwave model which takes dispersive terms into account is constructed for describing the motion of thin films with finite deviations from the middle surface. An exact periodic solution describing a nonlinear capillary wave is constructed within the framework of the model. Small deviations from the nonlinear capillary wave are described by a linear system with periodic coefficients. It is shown that for wave perturbation periods greater than a certain critical value the monodromy matrix of this system has eigenvalues whose absolute values are equal to unity. For perturbation periods less than the critical period the absolute value of one of the eigenvalues becomes greater than unity.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.