Exact soliton solutions for some nonlinear partial differential equations

Nonlinear partial differential equations (NPDEs) can be transformed into ordinary linear partial differential equations in the wave number domain. Explicit soliton solutions for some NPDEs can be obtained by subsequently solving these linear differential equations and by applying a cascade of (nonlinear) transformations to the solution of the linear differential equations. Thus, families of soliton solutions classes for the Tzitzéica equation, the sinh-Poisson equation and the unstable nonlinear Schrödinger (UNLS) equations are obtained.