Teoretičeskaâ i matematičeskaâ fizika, Tome 87 (1991) no. 1, pp. 40-47
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V. R. Kudashev; S. E. Sharapov. Inheritance of KdV symmetries under Whitham averaging and hydrodynamic symmetries of the Witham equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 87 (1991) no. 1, pp. 40-47. http://geodesic.mathdoc.fr/item/TMF_1991_87_1_a3/
@article{TMF_1991_87_1_a3,
author = {V. R. Kudashev and S. E. Sharapov},
title = {Inheritance {of~KdV} symmetries under {Whitham} averaging and hydrodynamic symmetries of the {Witham} equations},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {40--47},
year = {1991},
volume = {87},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1991_87_1_a3/}
}
TY - JOUR
AU - V. R. Kudashev
AU - S. E. Sharapov
TI - Inheritance of KdV symmetries under Whitham averaging and hydrodynamic symmetries of the Witham equations
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 1991
SP - 40
EP - 47
VL - 87
IS - 1
UR - http://geodesic.mathdoc.fr/item/TMF_1991_87_1_a3/
LA - ru
ID - TMF_1991_87_1_a3
ER -
%0 Journal Article
%A V. R. Kudashev
%A S. E. Sharapov
%T Inheritance of KdV symmetries under Whitham averaging and hydrodynamic symmetries of the Witham equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1991
%P 40-47
%V 87
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1991_87_1_a3/
%G ru
%F TMF_1991_87_1_a3
Explicit expressions that demonstrate the inheritance of some symmetries of the KdV equations by the Whitham equations for cnoidal KdV waves are obtained. A class of symmetries of Whitham equations of special form is found and described. Explicit expressions that describe a series of self-similar solutions of Whitham equations are obtained.
