20 citations · 37 across the 7 of their papers we have counts for
7 papers
Miura-reciprocal transformation and symmetries for the spectral problems of KdV and mKdV
Paz Albares, Pilar García Estévez
We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciproca…
Derivative non-linear Schrödinger equation: Singular manifold method and Lie symmetries
Paz Albares, Pilar García Estévez, Juan Domingo Lejarreta
We present a generalized study and characterization of the integrability properties of the derivative non-linear Schrödinger equation in 1+1 dimensions. A Lax pair is derived for t…
Reciprocal transformations and their role in the integrability and classification of PDEs
P. Albares, P. G. Estévez, C. Sardón
Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized vers…
Iterative symmetry search and reduction of a wave water model in dimensions
P. G. Estévez, J. D. Lejarreta, C. Sardón
We present the iterative classical point symmetry analysis of a shallow water wave equation in dimensions and that of its corresponding nonisospectral, two component Lax pair…
Miura-reciprocal transformations for non-isospectral Camassa-Holm hierarchies in dimensions
P. G. Estévez, C. Sardón
We present two hierarchies of partial differential equations in dimensions. Since there exist reciprocal transformations that connect these hierarchies to the Calogero-Bogoya…
Non-classical symmetries and the singular manifold method: A further two examples
Pilar G. Estevez, Pilar R. Gordoa
This paper discusses two equations with the conditional Painleve property. The usefulness of the singular manifold method as a tool for determining the non-classical symmetries tha…