Geodesic
Integrable Quasilinear Equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 233-246

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We develop a classification scheme for integrable third-order scalar evolution equations using the symmetry approach to integrability. We use this scheme to study quasilinear equations of a particular type and prove that several equations that were suspected to be integrable can be reduced to the well-known Korteweg–de Vries and Krichever–Novikov equations via a Miura-type differential substitution.
Keywords: classification of integrable differential equations, formal symmetry approach, differential substitutions. 
@article{TMF_2002_133_2_a8,
     author = {R. Hernandez Heredero},
     title = {Integrable {Quasilinear} {Equations}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {233--246},
     publisher = {mathdoc},
     volume = {133},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a8/}
}
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R. Hernandez Heredero. Integrable Quasilinear Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 233-246. http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a8/