Comments on whether nonlinear fractional partial differential equations have soliton solutions

Abstract

It is well known that many nonlinear integer-order partial differential equations (PDEs) have soliton solutions, this is an indisputable fact in the field of soliton theory. But do the corresponding nonlinear fractional-order PDEs also have soliton solutions? Some articles in recent publications show that some nonlinear fractional-order PDEs have soliton solutions. Are these results correct? Do the nonlinear fractional PDEs really have soliton solutions? In this paper, we will discuss this interesting topic and make our own views and related comments, meanwhile we sincerely invite peer experts to track and discuss this controversial issue.

Keywords

• Fractional-order nonlinear partial differential equation
• Soliton solution
• Chain rule of the fractional derivative
• Fractional complex transformation