Sech-polynomial travelling solitary-wave solutions of odd-order generalized KdV equations

A (2 m + 1)th-order generalized KdV equation is considered, where m is a positive integer. Four new explicit travelling solitary-wave solutions are obtained for the case m = 4. The case of arbitrary m ≥ 3 is considered; it is shown that, subject to certain restrictions on the coefficients in the equation, there are always at least two sech-polynomial type solutions.