Geodesic
A~limit symmetry of the~Korteweg--de Vries equation and its applications
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 277-287

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We discuss a symmetry of the Korteweg–de Vries (KdV) equation. This symmetry can be related to the squared eigenfunction symmetry by a limit procedure. As applications, we consider the similarity reduction of the KdV equation and a KdV equation with new self-consistent sources. We derive some solutions via a bilinear approach.
Keywords: symmetry, KdV equation, symmetry constraint, self-consistent source, bilinear method. 
@article{TMF_2010_163_2_a3,
     author = {Zhang Da-jun and Jian-bing Zhang and Qing Shen},
     title = {A~limit symmetry of {the~Korteweg--de} {Vries} equation and its applications},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {277--287},
     publisher = {mathdoc},
     volume = {163},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a3/}
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Zhang Da-jun; Jian-bing Zhang; Qing Shen. A~limit symmetry of the~Korteweg--de Vries equation and its applications. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 277-287. http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a3/