Painlevé property of general variable-coefficient versions of the Korteweg-de Vries and non-linear Schrödinger equations

Abstract General variable-coefficient versions of the Korteweg-de Vries (KdV) and non-linear Schrodinger (NLS) equations are shown to posses the Painleve property when their time-dependent coefficient functions are related by respective constraints. Under these constraints, found previously by Grimshaw in another context, the equations can be mapped to their well-known constant-coefficient versions. Transformations mapping the variable-coefficient versions to other modifications of the KdV and the NLS equations are discussed.

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