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SUMMARY:I. Melnikov (HSE Nizhny Novgorod\, Russia)
DTSTART:20261022T110000Z
DTEND:20261022T120000Z
DTSTAMP:20261026T225752Z
UID:mmandim/117
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/117/
 ">Pyramidal solitons in a generalized KdV equation</a>\nby I. Melnikov (HS
 E Nizhny Novgorod\, Russia) as part of Mathematical models and integration
  methods\n\n\nAbstract\nThe Korteweg – de Vries (KdV) equation is a clas
 sical model for describing long gravity waves on water and has among its s
 olutions solitons – solitary waves propagating at constant speed and int
 eracting elastically. The report discusses a generalized KdV equation in w
 hich the nonlinear term is given by an arbitrary smooth function\, modelin
 g a broader class of problems. The form of a solitary wave type solution i
 n this equation may differ from the classical solitons of the KdV equation
 \; in particular\, depending on the nonlinearity\, the number of inflectio
 n points may increase (we call such solutions pyramidal).\nPyramidal solit
 ons can arise in modeling internal waves and in problems of plasma physics
 .\nTheir stability and interactions are studied using generalizations of t
 he Gardner equation and other equations from the generalized KdV family.\n
 \nThis is joint work with E. Pelinovsky.\n\n The main results of this work
  were published in the articles:\n\n1. I. Melnikov\, E. Pelinovsky\, Pyram
 idal solitons: existence\, instability\, and interactions\, Nonlinear Dyn.
  (2026)\, 114:934.\n\n2. I. Melnikov\, Soliton solution classification in 
 the generalized Korteweg–de Vries equation\, Nonlinear Dyn. (2025)\, 113
 :32641–32648.\n
LOCATION:https://researchseminars.org/talk/mmandim/117/
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