Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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

A peer-reviewed article of this Preprint also exists.

Samokhin, A. On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations. Symmetry 2021, 13, 220. Samokhin, A. On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations. Symmetry 2021, 13, 220.

Journal reference: Symmetry 2021, 13, 220
DOI: 10.3390/sym13020220

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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