NUMERICAL SOLUTIONS OF SPACE FRACTIONAL VARIABLE-COEFFICIENT KdV-MODIFIED KdV EQUATION BY FOURIER SPECTRAL METHOD

Today, most of the real physical world problems can be modeled with variable-coefficient KdV-modified KdV (vcKdV-mKdV) equation. Besides, the solution methods and their reliabilities are the most important. Therefore, a high precision numerical method is always needed. In this paper, Fourier spectral method is applied to solve the space fractional generalized vcKdV-mKdV equation and the influence of fractional orders on numerical solution of the space fractional generalized vcKdV-mKdV equation is investigated. Numerical simulations in different situations of equation are conducted, including the propagation and interaction of the generalized ball-type, kink-type and periodic-depression solitons. From the numerical experiments pondered here and compared with the other methods, it is found that the numerical solutions match well with the exact solutions, which demonstrate that the Fourier spectral method is a satisfactory and efficient algorithm.