New periodic solitary wave solutions for an extended generalization of Vakhnenko equation

AbstractHere, we propose an improvement ansatz in three-wave method, then applying this ansatz to an extended generalization of Vakhnenko equation, we obtain a new periodic type of three-wave solutions including periodic two-solitary solution, doubly periodic solitary solution and breather two-solitary solution, respectively. These results show that the three-wave type of ansatz approach is an effective and simple method for seeking three-wave solutions and two-wave solutions of higher dimensional nonlinear evolution equations