RESUMEN

We have analysed the equations of one-dimensional gas dynamics from the point the view of the Lie-Backlund transformation. The important outcome of our analysis is that these extended symmetry transformations can have arbitrary functional form in terms of jet variables. Both the cases of coupled and decoupled sets of equations have been considered.

RESUMEN

We have made a Painleve for some coupled KdV systems, other than that of Hirota and Satsuma. These equations are interesting from many aspects. Due to the coupling with the other non-linear equation sometimes the singularity on the solution manifold becomes logarithmic. Also it is seen that the position on the resonances depends upon coupling parameters. We have analyzed in detail the structure of resonances and the formation of the coefficients at the resonances positions following the methodology of Ablowitz et al.