On the modulational of Schamel nonlinear Schrödinger equation and the associated envelope excitations in a degenerate relativistic quantum complex plasma

The modulational instability (MI) of Schamel/modified nonlinear Schrödinger equation (SNLSE) or (mNLSE) and the associated envelope excitations, including bright solitons in a multicomponent dense plasma consisting of relativistically degenerate electrons, trapped ions, and non-degenerate dust species are reported. A conventional multiple scales perturbative technique is utilized to get a SNLSE. This equation is different from the standard NLSE which the SNLSE has a nonlinear term with fractional order (3/2). The MI criteria are derived in detail. Also, the occurrence of envelope solitary wave and the effects of the different physical parameters on its profile are briefly discussed. The current results are advantageous to understand the mechanism of the propagation of the envelope excitations in complex plasmas with trapped ions and relativistically degenerate electrons, such as those observed in space observations and laboratory complex plasma.