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 ).
Publisher Copyright:
© 2015 Elsevier B.V.All rights reserved.
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
SN - 0375-9601
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
IS - 22-23
ER -