This article is cited in 3 papers

Integrable Quasilinear Equations

R. Hernandez Heredero

Universidad Complutense, Departamento de Fisica Teorica II

Abstract: 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.

DOI: 10.4213/tmf393

 English version: Theoretical and Mathematical Physics, 2002, 133:2, 1516–1528

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