NONLINEAR SCHRÖDINGER EQUATION WITH DISPERSION AND POTENTIAL OF THE GENERAL FORM: EXACT SOLUTIONS AND REDUCTIONS
https://doi.org/10.26583/vestnik.2024.6.3
EDN: OEBIJV
Abstract
The nonlinear Schrödinger equation of a general form is investigated, in which the chromatic dispersion and the potential are given by two arbitrary functions. The equation under consideration is a natural generalization of a wide class of related nonlinear equations that are often encountered in various sections of theoretical physics, including nonlinear optics, superconductivity, and plasma physics. Exact solutions of the nonlinear Schrödinger equation of general form are found, which are expressed in quadratures. One-dimensional non-symmetry reductions are described, which reduce the studied partial differential equation to simpler ordinary differential equations or systems of such equations. Special attention is paid to equations whose dispersion is given by a power function. The exact solutions obtained in this work can be used as test problems intended to assess the accuracy of numerical methods for integrating nonlinear equations of mathematical physics.
Keywords
nonlinear Schrödinger equation,
general nonlinear PDEs,
nonlinear optics,
exact solutions,
solutions in quadratures,
generalized separable solutions,
non-symmetry reductions
Supporting agencies: The work was carried out on the topics of the state assignment (NoNo state registration 124012500440-9 and FSWU-2023-0031)
About the Authors
A. D. Polyanin
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
Russian Federation
Russian Federation
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
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Review
For citations:
Polyanin A.D., Kudryashov N.A. NONLINEAR SCHRÖDINGER EQUATION WITH DISPERSION AND POTENTIAL OF THE GENERAL FORM: EXACT SOLUTIONS AND REDUCTIONS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2024;13(6):394-402. (In Russ.) https://doi.org/10.26583/vestnik.2024.6.3. EDN: OEBIJV
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