For a lattice Boussinesq equation,we introduce a simple-parameter invertible transformation by which the equation is transformed into an extended version.This new equation admits solitons and nonzero quasi-rational solutions,both in Casoratian form.These solutions can be reverted to those of the lattice Boussinesq equation.
The authors generalize the Cauchy matrix approach to get exact solutions to the lattice Boussinesq-type equations:lattice Boussinesq equation,lattice modified Boussinesq equation and lattice Schwarzian Boussinesq equation.Some kinds of solutions including soliton solutions,Jordan block solutions and mixed solutions are obtained.
IsospectrM and non-isospectral hierarchies related to a variable coefficient Painlev6 integrable Korteweg-de Vries （KdV for short） equation are derived. The hier- archies share a formal recursion operator which is not a rigorous recursion operator and contains t explicitly. By the hereditary strong symmetry property of the formal recur- sion operator, the authors construct two sets of symmetries and their Lie algebra for the isospectral variable coefficient Korteweg-de Vries （vcKdV for short） hierarchy.
