Abstract
This paper deals with the nonlinear Schrödinger equation (NLSE) with logarithmic and power nonlinearities as well as with several generalizations of NLSE—Biswas-Milovic̆ equation and others. Solutions of special form are written explicitly via hyperbolic, Jacobi elliptic, Weierstrass and Legendre elliptic functions of the three kinds. Generalized (distribution) solutions for the logarithmic Schrödinger equation containing one or two delta potentials are constructed too. The Biswas-Milovic̆ equation is ill-posed in the periodic Sobolev space H s with respect to the space variable x for s < 0.
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Popivanov, P., Slavova, A. (2020). Exact Formulas to the Solutions of Several Generalizations of the Nonlinear Schrödinger Equation. In: Boggiatto, P., et al. Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36138-9_23
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DOI: https://doi.org/10.1007/978-3-030-36138-9_23
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