  The degenerate coupled multi-KdV equations for coupled multiplicity l=3 are
studied. The equations also known as three fields Kaup-Boussinesq equations are
considered for invariant analysis and conservation laws. The classical Lie's
symmetry method is used to analyze the symmetries of equations. Based on
Killing's form which is invariant of adjoint action, the full classification
for Lie algebra is presented. Further, one-dimensional optimal group
classification is used to obtain invariant solutions. Besides this, using
general theorem proved by Ibragimov we find several nonlocal conservation laws
for these equations. The conserved currents obtained in this work can be useful
for the better understanding of some physical phenomena modeled by the
underlying equations.
