Describing dynamics of nonlinear axisymmetric waves in dispersive media with new equation

Dmitry G. Arkhipov, Georgy A. Khabakhpashev, Vladimir E. Zakharov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A single nonlinear partial differential equation of the wave type for an axisymmetric case is obtained by the introduction of special auxiliary function. In contrast to cylindrical Korteweg-de Vries equation, new equation describes centrifugal and centripetal waves not only far from the center, but in its vicinity as well. With the use of this equation a number of specific problems on the evolution of the free surface disturbances are numerically solved for the cases of a horizontal bottom and a drowned concave. The research also demonstrates the difference between the results of calculations on the base of the complete equation and on the basis of the linearized equation.

Original languageEnglish (US)
Pages (from-to)1414-1417
Number of pages4
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number22-23
StatePublished - Jul 17 2015


  • Axisymmetric disturbance
  • Centrifugal wave
  • Centripetal wave
  • Interaction of disturbances
  • Nonlinear wave
  • Transformation of disturbance

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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