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We present an approach to the bright soliton solution of the NLS equationfrom the standpoint of introducing a constant potential term in the equation.We discuss a `nongauge' bright soliton for which both the envelope and thephase depend only on the traveling variable. We also construct a family ofgeneralized NLS equations with solitonic sech^p solutions in the travelingvariable and find an exact equivalence with other nonlinear equations, such asthe Korteveg-de Vries and Benjamin-Bona-Mahony equations when p=2

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