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The natural world involves many complex phenomena with a wide range of mathematical applications. Nonlinear partial differential equations (NPDEs) have a large impact on the study of nonlinear physical processes. NPDEs are mostly analyze the behavior of waves in the form of solitons and solitary waves. Indeed, 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 book proposes a numerical approach for finding solitary wave solution for some models in nonlinear phenomena. The solutions of these models are approximated via the finite difference technique and the localized radial basis functions (RBFs). The RBFs methods can be implemented both globally and locally. The global collocation techniques impose a large computational burden because a dense algebraic system must be calculated. The proposed technique is based on decomposing the initial domain into a number of subdomains using kernel approximation on each subdomain. Numerical results are given to clarify the efficiency and accuracy of the proposed method.