TY - JOUR

T1 - Describing dynamics of nonlinear axisymmetric waves in dispersive media with new equation

AU - Arkhipov, Dmitry G.

AU - Khabakhpashev, Georgy A.

AU - Zakharov, Vladimir E.

N1 - Funding Information:
We are grateful to E.A. Kuznetsov, L.A. Ostrovsky, E.N. Pelinovsky, and Yu.A. Stepanyants for valuable discussions of this investigation, and to the reviewer for his comments that allowed significantly improving this article. The study was financed by the Russian Science Foundation (grant No. 14-22-00174 ).

PY - 2015/7/17

Y1 - 2015/7/17

N2 - 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.

AB - 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.

KW - Axisymmetric disturbance

KW - Centrifugal wave

KW - Centripetal wave

KW - Interaction of disturbances

KW - Nonlinear wave

KW - Transformation of disturbance

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U2 - 10.1016/j.physleta.2015.03.010

DO - 10.1016/j.physleta.2015.03.010

M3 - Article

AN - SCOPUS:84940001479

VL - 379

SP - 1414

EP - 1417

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 22-23

ER -