Publication:
Comparison of the Effectiveness of Different Methods for Constructing Exact Solutions to Nonlinear PDEs. Generalizations and New Solutions

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W2942420476.pdf(306.65 KB)
Дата
2019
Авторы
Polyanin, Andrei D.
Journal Title
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Научные группы
Организационные подразделения
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Организационная единица
Институт интеллектуальных кибернетических систем
Цель ИИКС и стратегия развития - это подготовка кадров, способных противостоять современным угрозам и вызовам, обладающих знаниями и компетенциями в области кибернетики, информационной и финансовой безопасности для решения задач разработки базового программного обеспечения, повышения защищенности критически важных информационных систем и противодействия отмыванию денег, полученных преступным путем, и финансированию терроризма.
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Аннотация
The paper shows that, in looking for exact solutions to nonlinear PDEs, the direct method of functional separation of variables can, in certain cases, be more effective than the method of differential constraints based on the compatibility analysis of PDEs with a single constraint (or the nonclassical method of symmetry reductions based on an invariant surface condition). This fact is illustrated by examples of nonlinear reaction-diffusion and convection-diffusion equations with variable coefficients, and nonlinear Klein-Gordon-type equations. Hydrodynamic boundary layer equations, nonlinear Schrodinger type equations, and a few third-order PDEs are also investigated. Several new exact functional separable solutions are given. A possibility of increasing the efficiency of the Clarkson-Kruskal direct method is discussed. A generalization of the direct method of the functional separation of variables is also described. Note that all nonlinear PDEs considered in the paper include one or several arbitrary functions.
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Цитирование
Polyanin, Andrei D. Comparison of the Effectiveness of Different Methods for Constructing Exact Solutions to Nonlinear PDEs. Generalizations and New Solutions / Polyanin, AndreiD // Mathematics. - 2019. - 7. - № 5. - 10.3390/math7050386
URI
https://www.doi.org/10.3390/math7050386
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85072563400&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000472664400008
 https://openrepository.mephi.ru/handle/123456789/18334
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