Solitary waves in the nonlinear Schrödinger equation with spatially modulated Bessel nonlinearity

Using multivariate self-similarity transformation, we construct explicit spatial bright and dark solitary wave solutions of the generalized nonlinear Schrodinger equation with spatially Bessel-modulated nonlinearity and an external potential. Special kinds of explicit solutions, such as periodically breathing bright and dark solitary waves, are discussed in detail. The stability of these solutions is verified by means of direct numerical simulation.

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