Nongauge bright soliton of the nonlinear Schrödinger (NLS) equation and a family of generalized NLS equations

We present an approach to the bright soliton solution of the nonlinear Schrodinger (NLS) equation from the standpoint of introducing a constant potential term in the equation. We discuss a “nongauge” bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sechp solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg–de Vries (KdV) and Benjamin–Bona–Mahony (BBM) equations when p = 2.