In this paper, we construct a reciprocal transformation for the Geng-Xue equation and show that, with help of this transformation, we relate the first negative flow of the modified Boussinesq hierarchy to the Geng-Xue equation. Furthermore, we analyze the construction of conserved quantities and present new ones. [ABSTRACT FROM AUTHOR]
In this paper, we numerically investigate the dynamics of the solitary waves in the presence of damping and external stochastic forces for the improved Boussinesq equation. The hydrodynamical and Stokes damping will be considered respectively. Since the analytic solutions for the considered problems are not available, Monte Carlo method will be used in random space and finite volume element method will be used in physical space. Numerical results demonstrate that solitary wave profile is not strongly affected by the Gaussian white noise in our study. The average of the velocity of the solitary waves is very close to that for the deterministic case. [ABSTRACT FROM AUTHOR]