Abstract
In this paper, we present the simplified version of the extended sinh-Gordon equation expansion method. The newly proposed approach is based on the well-known sinh-Gordon equation and a travelling wave transformation. We successfully employed this approach to the (2+1)-dimensional nonlinear Chiral Schrodinger's and various solitary wave solutions to the studied nonlinear model are successfully constructed. The (2+1)-dimensional nonlinear Chiral Schrodinger's equation describes the edge states of the fractional quantum hall effect. The 2D and 3D surfaces of some of the obtained solutions are plotted.
Highlights
K=1 m θ ssinhi(θ)coshj(θ) s = 0, 1, 0 ≤ k ≤ m 0 ≤ j ≤ m mo q = Ψ(ξ)eiΩ, ξ = αx + βy − θt, Ω = rx + sy + ωt + φ θ = 2a(αr + βs) a(α2 + β2)Ψ + 2(rb1 + sb2)Ψ3 − (a(r2 + s2) + ω)Ψ = 0
4(αr + βs) × i sech αx + βy + 2s2 + 2r2 + α2 + β2 t
2 (a(2s2 + α2 + β2) + 2ω)b21 + 2as2b22 α × i sech αx + βy − 2a βs −
Summary
K=1 m θ ssinhi(θ)coshj(θ) s = 0, 1, 0 ≤ k ≤ m 0 ≤ j ≤ m mo q = Ψ(ξ)eiΩ, ξ = αx + βy − θt, Ω = rx + sy + ωt + φ θ = 2a(αr + βs) a(α2 + β2)Ψ + 2(rb1 + sb2)Ψ3 − (a(r2 + s2) + ω)Ψ = 0
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