Galerkin methods for the Davey–Stewartson equations

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

“…Some works tackle the elliptic-hyperbolic form of the DSS, and present finite-difference schemes in which the energy is conserved throughout time [16]. A numerical solution for the DSS based on Galerkin's method, finite time steps, and an extrapolated Crank-Nicolson scheme is provided in [17,18]. In that work, a decoupled semi-implicit multistep scheme is implemented to improve accuracy.…”

Optical soliton solutions of nonlinear Davey-Stewartson equation using an efficient method

“…This important system of equations has attracted the attention of many researchers. For example, the line soliton [4], the semi-inverse variational principle method (SIVPM), the improved tan(φ/2)-expansion method (ITEM) along with the generalized G /G-expansion method (GGM) [5], the G'/G method and the 1-soliton solution [6], the Galerkin methods [7], the extended tanh-function method [8], the generalized Kudryashov method [9], the traveling wave solutions [10], the first integral method [11], the solitary wave solution [12], the dynamical system method [13], the traveling waves solution and the exponential function method [14], the inverse scattering transform method and the soliton solutions [15], the self-similar solutions [16], the bilinear method [17,18], the single soliton and multi-soliton solutions [19], the G /G -expansion method [20], the generalized tan(φ/2) method and the He's semi-inverse variational method [21], and the bifurcation method [22,23]. Others popular techniques can be found in Ref.…”