Analytical soliton solutions for the (2 + 1)-perturbed and higher order cubic–quintic nonlinear Schrödinger equations

In this paper, a comprehensive analysis of traveling wave solutions of two nonlinear Schrödinger type equations are carried out with help of three different integration techniques namely the tanh–coth, Kudryashov and sine–cosine methods. These equations include the (2 + 1)-dimensional perturbed nonlinear Schrödinger’s equation and cubic–quintic nonlinear Schrödinger’s equation. The obtained travelling wave solutions are in the form of rational function solutions, trigonometric function solutions, exponential function solutions and hyperbolic function solutions. Our proposed results showed that these techniques are reliable to study the nonlinear PDEs in fiber optics. The higher order cubic–quintic nonlinear Schrödinger equation (NLSE) explains the transmission of incredibly low signals and broadband communications that stretch into the spectral region, as well as the doping of optical fiber and the encryption of data in optical fibers.