Abstract
Gaussian spatial soliton solutions of both the constant-coefficient and variable-coefficient (2 + 1)-dimensional nonlinear Schrodinger equations in quintic–septimal nonlinear materials with different diffractions are presented under two kinds of $${\mathcal {P}}{\mathcal {T}}$$ -symmetric potentials. The linear stability analysis and direct numerical simulation are jointly utilized to investigate the stability for analytical solutions of the constant-coefficient equation. Results from the linear stability analysis and the direct numerical simulation possess a high degree of consistency, that is, the stable case for Gaussian spatial solitons of the constant-coefficient equation appears only in the defocusing quintic and focusing septimal nonlinear material. Moreover, reconstruction of stable Gaussian spatial solitons of the variable-coefficient equation is studied based on the expression of the effective propagation distance Z(z) by choosing an appropriate form of diffraction $$\beta _1(z)$$ .
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