integrability, the linearized equation is also solved exactly[@ChenChenHuang; @Kovrizhin], and the phonon excitations are shown to be completely reflectionless against a soliton for *any* excitation energy. Thus, the problem is trivial in this case. However, when the nonlinear term is generalized, the phonon has a finite reflection coefficient in general. It is worthy to note that the soliton decay dynamics in the laser-trapped quasi-1D BEC has been well explained by the *quintic* term, which appears as a second-order perturbation of the trapping effect[@Muryshev; @SinhaChernyKovrizhinBrand; @KhaykovichMalomed], and yields the frictional force between thermal excitation clouds and solitons[@Muryshev; @SinhaChernyKovrizhinBrand]. Thus, knowing the scattering properties between solitons and linearized excitations is essential to understand and control the transport of solitons, that is, the transport of stable wave packets. We also mention that the theory of nonpolynomial NLS equation is formulated to describe the confinement effect[@SalasnichParolaReatto; @MateoDelgado; @MateoDelgadoAnnPhys; @Salasnich]. The quintic NLS also appears in an effective mean-field description of the Tonks-Girardeau gas[@Kolomeisky].\
The NLS equation with an integrability breaking factor is also interesting from the viewpoint of an infinite-dimensional dynamical system and the bifurcation theory. When the potential barrier is added in the cubic NLS equation, there exist stable and unstable stationary supercurrent-flowing 