Soliton and Rogue Wave Solution of the New Nonautonomous Nonlinear Schrdinger Equation

In this paper,a new type(or the second type) of transformation which is used to map the variable coefficient nonlinear Schr(o|¨)dinger(VCNLS) equation to the usual nonlinear Schr(o|¨)dinger(NLS) equation is given.As a special case,a new kind of nonautonomous NLS equation with a t-dependent potential is introduced.Further,by using the new transformation and making full use of the known soliton and rogue wave solutions of the usual NLS equation,the corresponding kinds of solutions of a special model of the new nonautonomous NLS equation are discussed respectively. Additionally,through using the new transformation,a new expression,i.e.,the non-rational formula,of the rogue wave of a special VCNLS equation is given analytically.The main differences between the two types of transformation mentioned above are listed by three items.