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Allowed transformations and symmetry classes of variable coefficient Korteweg-de Vries equations

Authors
Journal
Physics Letters A
0375-9601
Publisher
Elsevier
Publication Date
Volume
167
Issue
3
Identifiers
DOI: 10.1016/0375-9601(92)90199-v

Abstract

Abstract The symmetry group of the variable coefficient KdV equation u t + f( x, t) uu x + g( x, t) u xxx =0 is shown to be at most four-dimensional and this occurs only if the functions f and g can be transformed into constants. All VCKdV equations with three-dimensional symmetry groups are identified. VCKdV equations are classified into conjugacy classes under “allowed transformations”, leaving the form invariant but changing the functions f and g.

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