On the solitary wave dynamics of complex Ginzburg–Landau equation with cubic nonlinearity

Constructing new wave solutions to the $$(2 + 1)$$-dimensional Davey–Stewartson equation (DSE) which arises in fluid dynamics

“…3, 4, we draw 2D and 3D surfaces of q 5 ( ) and r 5 ( ) in Eq. (20), which show the dynamics of solutions with proper parameters. Moreover, such hyperbolic functions are of different physical meanings as well.…”

“…Shen et al [11] have conducted a new construction procedure based on nonlinear variable separation [17]. This method has been successfully applied to obtain exact solutions for a variety of nonlinear PDEs [17][18][19][20].…”

The Application of the exp⁡(-Φ(ξ))-Expansion Method for Finding the Exact Solutions of Two Integrable Equations

“…Nonlinear evolution equations (NLEEs) are one of the fastest developing zones of research in the field of science and engineering, especially in mathematical biology, nonlinear optics, optical fiber, fluid mechanics, solid state physics, biophysics, chemical physics, chemical kinetics, etc. Many effective methods have been proposed to solve the NLEEs, such as the Hirota method [1], Hereman-Nuseir method [2], inverse scattering transformation [4], Painlevé technique [5], Bäcklund transformation [6], Darboux transformation [7,8], Binary-Bell-polynomial scheme [9], first integral method [10,11], ( / )−expansion method [12], the exp(−Φ( )) expansion method [13], Exp-function method [14], ansatz method [15], sine-Gordon expansion method [16,17], the trial equation method [18,19], homotopy asymptotic [20], and so on.…”