Soliton Kernels for Solving PDEs

There are many important applications in the fields of computer experiments, response surface modeling, finance and image processing, where some special types of nonstandard kernels performed better than standard kernels. These kernels are more appropriate than standard kernels when looking at special solutions of partial differential equations (PDEs). For example some nonlinear time-dependent PDEs have soliton like solutions, so soliton kernels would more suit to approximate the solution. In this work, we recover the solution of equal width equation using soliton kernels.