621 research outputs found
Classical Lie symmetries and reductions of a nonisospectral Lax pair
The classical Lie method is applied to a nonisospectral problem associated
with a system of partial differential equations in 2+1 dimensions (Maccari A,
J. Math. Phys. 39, (1998), 6547-6551). Identification of the classical Lie
symmetries provides a set of reductions that give rise to different nontrivial
spectral problems in 1+1 dimensions. The form in which the spectral parameter
of the 1+1 Lax pair is introduced is carefully described.Comment: 11 pages (v2: A typo corrected in the authors' names
Non-classical symmetries and the singular manifold method: A further two examples
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 that reduce the equations to ordinary differential
equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics
Miura Transformation between two Non-Linear Equations in 2+1 dimensions
A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by
different authors is shown to be nothing but the modified version of the
Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and
techniques based upon the Painleve Property leading to the Double Singular
Manifold Expansion we shall find the Miura Transformation which converts the
2LDW Equation into the GLDW Equation. Through this Miura Transformation we
shall also present the Lax pair of the 2LDW Equation as well as some
interesting reductions to several already known integrable systems in 1+1
dimensions.Comment: 14 pages, latex. Journal of Mathematical Physics (to appear
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