Soliton solutions for the fifth-order Kaup–Kupershmidt equation

In this paper, analytical solutions of the fifth-order Kaup–Kupershmidt (KK) equation have been derived via the auxiliary function in conjunction with the bilinear method. These solutions have not previously been obtained in any other literatures. Propagation and interactions of the one-, two- and three-soliton solutions have been presented. The velocity of one soliton is related to the physical parameter a 1 , and the amplitude of the soliton is related to the parameters a 1 and A 1 . The velocities of two solitons are related to the parameters a 1 and a 2 , and the amplitudes of two solitons are related to the parameters a 1 , a 2 , M 1 and M 2 . The physical parameters a j have effect on the numbers of the interacting points and distances of the solitons before and after the interactions. The signs of the physical parameters a j also have effect on the hole of the interactions. The velocities and amplitudes of three solitons are both related to the parameters a j .