Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@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/}
}
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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/