Abstract
A variable-coefficients nonisospectral nonlinear Schrödinger (vc-nNLS) equation is investigated. Integrable background in the framework of the Lax pair with a time-dependent spectral parameter satisfying a generalized Ricatti equation is given. Solutions are given in terms of the double Wronski determinant where the Hirota method is employed. Moreover, different sorts of solutions are provided. In particular, employing the freedom of choosing the variable-coefficients, illustrative examples depicting localized wave solutions are presented.
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