N-soliton solutions for the Vakhnenko equation and its generalized forms

In this paper, we present an analytic study for the nonlinear Vakhnenko equation, a generalized Vakhnenko equation and a modified generalized Vakhnenko equation. The simplified form of the bilinear method, established by Hereman and Nuseir (1997 Math. Comput. Simul. 43 13-27), will be used to formally derive multiple soliton solutions and multiple singular soliton solutions for each equation. The resonance phenomenon is examined for each model.