Stability switching at transcritical bifurcations of solitary waves in generalized nonlinear Schrödinger equations

► Stability of solitary waves near transcritical bifurcations in GNLS equations is determined. ► Stability switching at the bifurcation point is analytically proved. ► Explicit analytical formulae for linear-stability eigenvalues are also derived. ► Numerical examples are given which confirm the analytical theory.