Conservative difference scheme for the nonlinear dispersive generalized regularized long-wave (GRLW) equation is proposed. Existence of its difference solutions has been shown. It is proved by the discrete energy method that the difference scheme is uniquely solvable, unconditionally stable and the convergence is of second-order in the maximum norm. The particular case known as the modified regularized long-wave (MRLW) equation is also discussed numerically in details. Furthemore, three invariants of motion are evaluated to determine the conservation properties of the problem. Interaction of two and three solitary waves are shown. Some numerical examples are given in order to validate the theoretical results.

提出了非线性色散广义正则长波方程的守恒差分格式。已经证明了其差分解的存在性。通过离散能量方法证明了差分方案是唯一可解的，是无条件稳定的，并且在最大范数下收敛是二阶的。还详细地讨论了称为修正正则化长波（MRLW）方程的特殊情况。此外，对运动的三个不变量进行了评估，以确定问题的守恒性质。显示了两个和三个孤立波的相互作用。给出一些数值例子以验证理论结果。