2015/06/24 by P. G. Estévez, Estévez, P. G., C. Sardón +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1506.07428
arxiv created 2015/08/03 · arxiv updated 2015/08/04
The non-isospectral problem (Lax pair) associated with a hierarchy in 2+1 dimensions that generalizes the well known Camassa-Holm hierarchy is presented. Here, we have investigated the non-classical Lie symmetries of this Lax pair when the spectral parameter is considered as a field. These symmetries can be written in terms of five arbitrary constants and three arbitrary functions. Different similarity reductions associated with these symmetries have been derived. Of particular interest are the reduced hierarchies whose 1+1 Lax pair is also non-isospectral.