Abundant soliton solutions for the Kundu–Eckhaus equation via tan(ϕ(ξ))-expansion method

In this paper, the improved tan(Φ(ξ)/2)tanΦ(ξ)/2-expansion method is proposed to seek more general exact solutions of the Kundu–Eckhaus equation. Being concise and straightforward, this method is applied to the nonlinear Kundu–Eckhaus equation. The exact particular solutions containing five types hyperbolic function solution (exact soliton wave solution), trigonometric function solution (exact periodic wave solution), rational exponential solution (exact singular kink-type wave solution), logarithmic solution and rational solution (exact singular cupson wave solution). We obtained further solutions comparing this method with other methods. The results demonstrate that the new tan(Φ(ξ)/2)tanΦ(ξ)/2-expansion method is more efficient than the Ansatz method applied by Baskonus et al. [16]. Recently this method developed for searching exact travelling wave solutions of nonlinear partial differential equations. Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important role in engineering and physics fields.