MULTIDIMENSIONAL NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL AND DISPERSION OF THE GENERAL FORM: EXACT SOLUTIONS AND REDUCTIONS
https://doi.org/10.26583/vestnik.2025.2.3
EDN: GOCPTB
Abstract
Multidimensional nonlinear Schrödinger equations of the general form are investigated, in which the potential and dispersion are specified by one or two arbitrary functions. The equations under consideration naturally generalize a number of related nonlinear partial differential equations that occur in various areas of theoretical physics, including nonlinear optics, superconductivity, and plasma physics. Multidimensional and one-dimensional non-symmetry reductions are described, which lead the studied nonlinear Schrödinger equations to simpler equations of lower dimension or ordinary differential equations (or systems of ordinary differential equations). Special attention is paid to finding solutions with radial symmetry. Using methods of generalized separation of variables, new exact solutions of two-dimensional and n-dimensional nonlinear Schrödinger equations of the general form, which are expressed in quadratures or elementary functions, are found.
Keywords
About the Authors
A. D. PolyaninRussian Federation
N. A. Kudryashov
Russian Federation
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Review
For citations:
Polyanin A.D., Kudryashov N.A. MULTIDIMENSIONAL NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL AND DISPERSION OF THE GENERAL FORM: EXACT SOLUTIONS AND REDUCTIONS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2025;14(2):116-130. (In Russ.) https://doi.org/10.26583/vestnik.2025.2.3. EDN: GOCPTB