On the Numerical Solution of Evolution Equation via Soliton Kernels

In application of kernel-based methods, some particular types of PDEs need some special types of kernels for their approximations. For example some nonlinear evolution equations describing wave processes in dispersive and dissipative media. These models may have soliton like solutions for example KdV equation. In such a situation some special types of kernels may perform better than standards kernels for example soliton kernels.