A new form of general soliton solutions and multiple zeros solutions for a higher-order Kaup–Newell equation

Due to higher-order Kaup-Newell (KN) system has more complex and diverse solutions than classical second-order flow KN system, the research on it attracted attention. In this paper, we consider a equation with third order dispersion quintic nonlinearity. Based theory of inverse scattering, matrix Riemann-Hilbert problem is established. Through dressing method, solution simple zeros without reflection constructed. particular, new form given, which direct simpler previous methods. addition, through determinant matrix, vivid diagrams dynamic analysis single soliton two are given in detail. Finally, by using technique limit, construct general case multiple zeros, examples for cases double triple single-double double-double especially shown.