Zobrazeno 1 - 10
of 302
pro vyhledávání: '"Polyanin, A. D."'
For the first time, Schr\"odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such nonlinear equation
Externí odkaz:
http://arxiv.org/abs/2411.19349
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class of relate
Externí odkaz:
http://arxiv.org/abs/2411.13713
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative examples ar
Externí odkaz:
http://arxiv.org/abs/2407.17995
Autor:
Polyanin, Andrei D.
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related equations
Externí odkaz:
http://arxiv.org/abs/2405.20474
Publikováno v:
In Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena February 2025 191
Publikováno v:
Mathematical Modeling and Computational Methods, 2021, No. 2, pp. 96-116 https://mmcm.bmstu.ru/articles/253
The problems of estimating the similarity index of mathematical and other scientific publications containing equations and formulas are discussed for the first time. It is shown that the presence of equations and formulas (as well as figures, drawing
Externí odkaz:
http://arxiv.org/abs/2201.09062