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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 163, Pages 81–95 (Mi into452)  

On analogs of wave catastrophe functions that are solutions of nonlinear integrable equations

B. I. Suleimanov

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa

Abstract: In this paper, we consider symmetry and isomonodromy properties of universal special solutions of integrable nonlinear evolution equations, which are analogs of standard wave catastrophe functions known for linear problems. We perform a comparative analysis of two different approaches to the choice of symmetries of integrable nonlinear equations, which can be applied to the study of such special solutions. Some examples are also presented.

Keywords: wave catastrophe function, nonlinear integrable equation, symmetries, recursion operator, method of isomonodromy deformation

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Bibliographic databases:
UDC: 517.925
MSC: 34Mxx

Citation: B. I. Suleimanov, “On analogs of wave catastrophe functions that are solutions of nonlinear integrable equations”, Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 81–95

Citation in format AMSBIB
\Bibitem{Sul19}
\by B.~I.~Suleimanov
\paper On analogs of wave catastrophe functions that are solutions of nonlinear integrable equations
\inbook Differential Equations
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 163
\pages 81--95
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into452}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4014977}


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