Variational discretizations for the generalized Rosenau-type equations

The generalized Rosenau-type equations include the Rosenau–RLW equation and the Rosenau–KdV equation, which both admit the third-order Lagrangians. In the Lagrangian framework, this paper presents the variational formulations of the generalized Rosenau-type equations as well as their multisymplectic structures. Based on the discrete variational principle, we construct the variational discretizations for solving the evolutions of solitary solutions of this class of equations. We simulate the motion of the single solitary wave, and also observe the different kind of collisions for the generalized Rosenau-type equations with various coefficients.