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We report a method of solving for canonical scalar field exact solution in anon-flat FLRW universe with barotropic fluid using non-linear Schr\"{o}dinger(NLS)-type formulation in comparison to the method in the standard Friedmannframework. We consider phantom and non-phantom scalar field cases withexponential and power-law accelerating expansion. Analysis on effectiveequation of state to both cases of expansion is also performed. We speculateand comment on some advantage and disadvantage of using the NLS formulation insolving for the exact solution.

Scalar field exact solutions for non-flat FLRW cosmology: A technique from non-linear Schr\"odinger-type formulation