Explicit solitary-wave solutions to generalized Pochhammer-Chree equations

For the solitary-wave solution u(xi) = u(x - vt + xi(0)) generalized Pochha mmer-Chree equation (PC equation) (I) u(tt) - u(uxx) + ru(xxt) - (a(1)u + a(2)u(2) + a(3)u(3))(xx) = 0, r,a(i ) = consts(r not equal 0), the integral(-infinity)(+infinity)[u'(xi)](2)dxi = 1/12rv(C+ - C-)(3)[3a(3) (C+ + C-) + 2a(2)], C+/- = lim(xi-->+/-infinity) u(xi), Is established, by which it is shown that the generalized PC equation (I) does not have bell p rofile solitary-wave solutions but may have kink profile solitary-wave solu tions. However a special generalized PC equation (II) u(tt) - u(uxx) - (a(1)u + a(2)u(2) + a(3)u(xx)(3)) = 0, a(i) = consts may have not only bell profile solitary-wave solutions, but also kink profi le solitary-wave solutions whose asymptotic values satisfy 3a(3)(C+ + C-) 2a(2) = 0. Furthermore all expected solitary-wave solutions are given, Fin ally same explicit hell profile solitary-wave solutions to another generali zed PC equation (III) u(tt) - u(uxx) - (a(1)u + a(3)u(3) + a(5)u(5))(xx) = 0, a(i =) const are proposed.