Solitary-wave solutions to a class of fifth-order model equations

This paper considers the fifth-order equation w(t) + w(xxxxx) + mu w(xxx) = f(w, w(x), w(xx))(x) for a certain class of nonlinearity f. A solitary-wave solution to this equation is a solution of the form w(x, t) = r(x - ct), where c is a constant and r vanishes as x - ct --> +/-infinity. It is shown that the equation has al least one non-zero solitary-wave solution when c < 0, mu < 2 root-c and a countably infinite family of geometrically distinct solitary-wave solutions when c < 0, -2 root-c < mu < 2 root-c.