Formula omitted]th-order rogue wave solutions for a variable coefficient Schrödinger equation in inhomogeneous optical fibers

Abstract

In investigation is a nonlinear Schrödinger equation with variable coefficients, which can describe pulse propagation in inhomogeneous optical fiber systems. The variable coefficients can used to control the dispersion and nonlinearity factors. Through extending Darboux transformation iteration algorithm, analytical Nth-order rogue wave solutions are obtained for the equation. Based on the two free variable coefficient function involved in the solutions, novel rogue waves can be excited by choosing them as specific functions. Polynomial and periodic functions are taken as examples to how to excite rich rogue wave solutions. The results show that as the orders of the rogue wave solutions increase, the spatio-temporal patterns become more complex, while the amplitudes also increase rapidly. These properties will play critical roles in high-capacity information transmission and signal amplification in optical systems.