  We study the Darboux and Laplace transformations for the
Boiti-Leon-Pempinelli equations (BLP). These equations are the (1+2)
generalization of the sinh-Gordon equation. In addition, the BLP equations
reduced to the Burgers (and anti-Burgers) equation in a one-dimensional limit.
Localized nonsingular solutions in both spatial dimensions and (anti) "blow-up"
solutions are constructed. The Burgers equation's "dressing" procedure is
suggested. This procedure allows us to construct such solutions of the BLP
equations which are reduced to the solutions of the dissipative Burgers
equations when $t\to \infty$. These solutions we call the BLP dissipative
structures.
