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The equation has a two-parameter family of solitary waves $$u_{\\omega,c}(t,x)=\\Phi_{\\omega,c}(x)e^{i\\omega t+\\frac{ic}2x-\\frac i{2\\sigma+2}\\int_0^x\\Phi_{\\omega,c}(y)^{2\\sigma}dy},$$ with $(\\omega,c)$ satisfying $\\omega>c^2/4$, or $\\omega=c^2/4$ and $c>0$. The stability theory in the frequency region $\\omega>c^2/4$ was studied previously. 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