Geodesic
Soliton solutions of the negative order modified Korteweg -- de Vries equation
The Bulletin of Irkutsk State University. Series Mathematics, Tome 47 (2024), pp. 63-77

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In this paper, we study the negative order modified Korteweg-de Vries (nmKdV) equation in the class of rapidly decreasing functions. In particular, we show that the inverse scattering transform technique can be applied to obtain the time dependence of scattering data of the operator Dirac with potential being the solution of the considered problem. We demonstrate the explicit representation of one soliton solution of nmKdV based on the obtained results.
Keywords: negative order modified Korteweg – de Vries equation, inverse scattering transform, scattering data, potential
Mots-clés : soliton, reflection coefficient. 
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     author = {Gayrat U. Urazboev and Iroda I. Baltaeva and Shoira E. Atanazarova},
     title = {Soliton solutions of the negative order modified {Korteweg} -- de {Vries} equation},
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     pages = {63--77},
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Gayrat U. Urazboev; Iroda I. Baltaeva; Shoira E. Atanazarova. Soliton solutions of the negative order modified Korteweg -- de Vries equation. The Bulletin of Irkutsk State University. Series Mathematics, Tome 47 (2024), pp. 63-77. http://geodesic.mathdoc.fr/item/IIGUM_2024_47_a4/