On the behavior of solutions of a class of nonlinear partial differential equations

The behavior of the steady-state (or the traveling wave) solutions for a cl ass of nonlinear partial differential equations is studied. The nonlinearit y in these equations is expressed by the presence of the convective term. I t is shown that the steady-state (or the traveling wave) solution may explo de at a finite value of the spatial (or the characteristic) variable. This holds whatever the order of the spatial derivative term in these equations. Furthermore, new special solutions of a set of equations in this class are also found.