Lax pairs and Bäcklund transformations for a coupled Ramani equation and its related system
The authors deal with the following coupled Ramani equation of the form \[ u_{xxxxxx}+ 15u_{xx}u_{xxx} +15u_xu_{xxxx} +45u_x^2u_{xx} -5(u_{xxxt} +3u_{xx}u_t +3u_xu_{xt}) -5u_{tt}+ 18w_x=0 \] \[ w_t-w_{xxx}- 3w_xu_x-3wu_{xx} =0. \] The authors show that this system is integrable in the sense of having a Bäcklund transformation and Lax pairs. Soliton solutions and rational solutions are also obtained.
scientific article; zbMATH DE number 1531195