Stability of the solitons for the one-dimensional Zakharov–Rubenchik equation

We prove the global well-posedness of the one-dimensional Zakharov–Rubenchik equation iBt+ωBxx−k(u−12vρ+q|B|2)B=0, θρt+(u−vρ)x=−k|B|2x, θut+(βρ−vu)x=12kv|B|2xin the space H2(R)×H1(R)×H1(R). We also prove the existence and the orbital stability of solitary wave solutions to the above equations.