Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Formation of Sawtooth Wavesfor Cylindrical and Sphericalkortweg-de Vries-Burgers Equations

Version 1 : Received: 22 December 2020 / Approved: 23 December 2020 / Online: 23 December 2020 (09:44:50 CET)

How to cite: Samokhin, A. Formation of Sawtooth Wavesfor Cylindrical and Sphericalkortweg-de Vries-Burgers Equations. Preprints 2020, 2020120579 (doi: 10.20944/preprints202012.0579.v1). Samokhin, A. Formation of Sawtooth Wavesfor Cylindrical and Sphericalkortweg-de Vries-Burgers Equations. Preprints 2020, 2020120579 (doi: 10.20944/preprints202012.0579.v1).

Abstract

For the KdV-Burgers equations on cylindrical and spherical waves the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary is studied. The equations describe a medium which is both dissipative and dispersive. Symmetries, invariant solutions and conservation laws are investigated. For an appropriate combination of dispersion and dissipation the asymptotic profile looks like a periodical chain of shock fronts with a decreasing amplitude (sawtooth waves). The development of such a profile is preceded by a head shock of a constant height and equal velocity which depends on spatial dimension as well as on integral characteristics of boundary condition; an explicit asymptotic for this head shock and a median of the oscillating part is found.

Subject Areas

Korteweg-de Vries-Burgers equation; cylindrical and spherical waves; saw-tooth solutions; periodic boundary conditions; head shock wave

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