Abstract
A variable coefficient, perturbed Korteweg-de Vries equation is considered, whose coefficients are slowly-varying in time, and for which the perturbation term represents various forms of dissipation. We construct asymptotic solutions for modulated periodic wavetrains using a multiple-scale expansion. The modulations are described by a nonlinear, non-homogeneous system of first-order partial differential equations for the parameters of the wavetrain that describes an extension to Whitham's modulation theory. We deal specifically with three forms of frictional terms representing (a) linear damping, (b) KdV-Burgers damping, and (c) boundary-layer damping. The initial condition is a step discontinuity which evolves into a disturbance resembling an undular bore. Then, in particular, we use this modulation theory to study the behaviour at and near the front and rear of the bore.
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 callDisclaimer: 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.
