Generalized Soliton Solutions to the Nonlinear Schrodinger Equation

Our primary goal is to provide a solution formula to the so-called derivative nonlinear Schrodinger
equation which has important physical applications in plasma physics and in nonlinearber optics. Using a
recent approach, wend our solutions in terms of three constant matrices with complex entries. We provide
some sucient conditions on our matrices for the analyticity of our solutions. Using the these matrices, we
nd three auxiliary matrices to construct our solution formula. We investigate the validity of our solution
formula as the matrix size becomes innite by rewriting our solution formula in terms of determinants
and by using the Fredholm determinant. We also prove that our solution is unchanged under similarity
transformation on our three constant matrices. In plasma physics, the derivative nonlinear Schrodinger
equation is a model for a low-frequency travelling oscillation of the ions and the magneticeld propagating
parallel to the ambient magneticeld. Inber optics, this equation models the propagation of very short
nonlinear input pulses, where the solution is the amplitude of the complexeld envelope at any particular
time.