SECH-POLYNOMIAL TRAVELING SOLITARY-WAVE SOLUTIONS OF ODD-ORDER GENERALIZED KDV EQUATIONS

A (2m + 1)th-order generalized KdV equation is considered, where m is a positive integer. Four new explicit travelling solitary-wave solutio ns are obtained for the case m = 4. The case of arbitrary m greater th an or equal to 3 is considered; it is shown that, subject to certain r estrictions on the coefficients in the equation, there are always at l east two sech-polynomial type solutions. (C) 1998 Elsevier Science B.V .