  In this work, a Cole-Hopf transformation based fourth-order
multiple-relaxation-time lattice Boltzmann (MRT-LB) model for d-dimensional
coupled Burgers' equations is developed. We first adopt the Cole-Hopf
transformation where an intermediate variable \theta is introduced to eliminate
the nonlinear convection terms in the Burgers' equations on the velocity
u=(u_1,u_2,...,u_d). In this case, a diffusion equation on the variable \theta
can be obtained, and particularly, the velocity u in the coupled Burgers'
equations is determined by the variable \theta and its gradient term
\nabla\theta. Then we develop a general MRT-LB model with the natural moments
for the d-dimensional transformed diffusion equation and present the
corresponding macroscopic finite-difference scheme. At the diffusive scaling,
the fourth-order modified equation of the developed MRT-LB model is derived
through the Maxwell iteration method. With the aid of the free parameters in
the MRT-LB model, we find that not only the consistent fourth-order modified
equation can be obtained, but also the gradient term $\nabla\theta$ can be
calculated locally by the non-equilibrium distribution function with a
fourth-order accuracy, this indicates that theoretically, the MRT-LB model for
$d$-dimensional coupled Burgers' equations can achieve a fourth-order accuracy
in space. Finally, some simulations are conducted to test the MRT-LB model, and
the numerical results show that the proposed MRT-LB model has a fourth-order
convergence rate, which is consistent with our theoretical analysis.
