Integration of the fractional modified Korteweg de Vries-sine-Gordon equation by the inverse scattering method

In this paper we investigate the fractional modified Korteweg de Vries-sine-Gordon equation and show the inverse scattering transform method can also be used to obtain soliton solutions of fractional modified Korteweg de Vries-sine-Gordon equation. It is illustrated the relationship between the wave velocity and the ϵ parameter for the fractional modified Korteweg de Vries-sine-Gordon equation in the case of one soliton solution, then this result was compared with fractional modified Korteweg de Vries equation, fractional sine-Gordon equation and the modified Korteweg de Vries-sine-Gordon equation.