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The $\frac{{G}^{\text{'}}}{G}$ method and 1-soliton solution of the Davey-Stewartson equation. (English) Zbl 1217.35171
Summary: This paper studies the Davey-Stewartson equation. The $\frac{{G}^{\text{'}}}{G}$ method is applied to carry out the integration of this equation. Subsequently, using the ansatz method this equation is integrated in $\left(1+2\right)$ dimensions with power law nonlinearity.
##### MSC:
 35Q55 NLS-like (nonlinear Schrödinger) equations 35C08 Soliton solutions of PDE
##### Keywords:
evolution equation; integrability; solitons
##### References:
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