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$\\frac{g_1^2 }{2} (\\bpsi \\gamma_{\\mu} \\psi)(\\bpsi \\gamma^{\\mu} \\psi)+ \\frac{g_2^2 }{2} (\\bphi \\gamma_{\\mu} \\phi)(\\bphi \\gamma^{\\mu} \\phi) + g_3^2 (\\bpsi \\gamma_{\\mu} \\psi)(\\bphi \\gamma^{\\mu} \\phi ). $ Writing the two components of the assumed solitary wave solution of these equations in the form $\\psi = e^{-i \\omega_1 t} 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