Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

Abstract

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schr¨odinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh- Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schr¨odinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.