Generalized reversible transformations and new nonautonomous higher order Nonlinear Schrödinger equation

Abstract

We investigate the nonautonomous higher order nonlinear Schrödinger equation and the reversible transformations. We propose a generalized reversible transformation between forced higher order NLSE with focusing and defocusing nonlinearity and free higher order NLSE. We have identified a set of new constraints among the higher order dispersion and nonlinear coefficients, which are preserved under the transformations. In the process, we find new higher order inhomogeneous equations. We obtain dark and bright solitons of the forced higher order NLSE directly using the transformation. The reversible transformations allow us to encompass NLSE and higher order NLSE (HNLSE) belonging to the class of nonisospectral family of inverse scattering problems to the class of isospectral NLSEs and study them under a general mathematical framework. We hope that our analysis provides a mathematical platform to study inhomogeneous NLS equations as well as opens up the possibility of new applications in physics.