Fractional quasi AKNS-technique for nonlinear space-time fractional evolution equations

摘要

This paper aims to formulate the fractional quasi-inverse scattering method. Also, we give a positive answer to the following question: can the Ablowitz-Kaup-Newell-Segur (AKNS) method be applied to the space-time fractional nonlinear differential equations? Besides, we derive the Backlund transformations for the fractional systems under study. Also, we construct the fractional quasi-conservation laws for the considered fractional equations from the defined fractional quasi AKNS-like system. The nonlinear fractional differential equations to be studied are the space-time fractional versions of the Kortweg-de Vries equation, modified Kortweg-de Vries equation, the sine-Gordon equation, the sinh-Gordon equation, the Liouville equation, the cosh-Gordon equation, the short pulse equation, and the nonlinear Schrodinger equation.