The \(N\)-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation). (Q1419205)

The goal of this paper is to present a generalization of the Vakhnenko equation, namely \[ {\partial\over\partial x} (D^2u+ qu^2+\beta u)+ qDu= 0,\quad D:= {\partial\over\partial t}+ u{\partial\over\partial x}, \] where \(\beta\) and \(q\) are arbitrary nonzero constants, and to find its \(N\)-soliton solution. The authors find not only loop soliton solutions, but himp-line and cusp-like soliton solutions.