On A New Form of Darboux-B\"acklund Transformation for DNLS Equation-Mixed and Rational Type Solutions

Abstract

A new form of Darboux-B\"acklund transformation and its higher order form is derived for Derivative Nonlinear Schrodinger Equation(DNLS). The new form arises due to the different form of Lax pair. It is observed that by a special choice of the eigenvalue of DB transformation one can generate a mixed form of solution(containing both algebraic and exponential dependence on (x, t) can be generated. On the other hand by adopting a new methodology due to Neugebauer et. al. it is found that purely rational solution can be constructed. The two different approach yields different class of solution and are compared.