Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the generalized Benjamin–Bona–Mahony–Burgers equation with dissipative term

In this paper, we investigate the asymptotic behavior of solutions to Cauchy problem with far field condititon for generalized Benjamin–Bona–Mahony–Burgers equation a fourth-order dissipative term. When corresponding Riemann hyperbolic part admits solution which consists single rarefaction wave, it is proved that tends toward wave as time goes infinity. We can further obtain same global stability Korteweg–de Vries–Benjamin–Bona–Mahony–Burgers term former one.