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 Citations (Scopus)


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
Pages (from-to)1414-1417
Number of pages4
JournalPhysics Letters A
Issue number22-23
Publication statusPublished - 17 Jul 2015
Externally publishedYes


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


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