The nonlinear wave phenomenon constitutes a significant research field and is a capable mathematical model for representing the transmission of energy in physical processes. This paper concentrates on the numerical solution for the nonlinear regularized long-wave and nonlinear extended Fisher–Kolmogorov models in two-space dimension. The solutions of these models are approximated via the finite difference technique and the localized radial basis function partition of unity. The association of the technique results in a meshfree method that does not require linearizing the nonlinear terms. In the first step, the partial differential equation (PDE) is transformed to a system of nonlinear ordinary differential equations (ODEs) by means of radial kernels. Subsequently, the nonlinear ODE system is approximated using a high-order ODE solver. The global collocation methods pose a considerable computational burden due to the calculation of the dense algebraic system. The proposed approach is based on a decomposition of the original domain into several subdomains via a kernel approximation on every subdomain. Numerical results such as the motion of single solitary and two solitary waves confirm the efficiency and accuracy of the method and are good agreement with the results of existing works in literature.

非线性波现象是一个重要的研究领域，是表示物理过程中能量传输的有效数学模型。本文主要研究二维非线性正则化长波和非线性扩展Fisher-Kolmogorov模型的数值解。这些模型的解是通过有限差分技术和统一的局部径向基函数划分来近似的。该技术的关联导致不需要线性化非线性项的无网格方法。第一步，偏微分方程 (PDE) 通过径向核转换为非线性常微分方程 (ODE) 系统。随后，非线性 ODE 系统使用高阶 ODE 求解器进行近似。由于密集代数系统的计算，全局搭配方法带来了相当大的计算负担。所提出的方法基于通过对每个子域的内核近似将原始域分解为几个子域。单个孤立波和两个孤立波的运动等数值结果证实了该方法的效率和准确性，并且与文献中现有工作的结果具有良好的一致性。