  A general lattice Boltzmann (LB) model is proposed for solving nonlinear
partial differential equations with the form $\partial_t \phi+\sum_{k=1}^{m}
\alpha_k \partial_x^k \Pi_k (\phi)=0$, where $\alpha_k$ are constant
coefficients, and $\Pi_k (\phi)$ are the known differential functions of
$\phi$, $1\leq k\leq m \leq 6$. The model can be applied to the common
nonlinear evolutionary equations, such as (m)KdV equation, KdV-Burgers
equation, K($m,n$) equation, Kuramoto-Sivashinsky equation, and Kawahara
equation, etc. Unlike the existing LB models, the correct constraints on
moments of equilibrium distribution function in the proposed model are given by
choosing suitable \emph{auxiliary-moments}, and how to exactly recover the
macroscopic equations through Chapman-Enskog expansion is discussed in this
paper. Detailed simulations of these equations are performed, and it is found
that the numerical results agree well with the analytical solutions and the
numerical solutions reported in previous studies.
