On a countable sequence of homoclinic orbits arising near a saddle-center point

Autor:	Baldomá, Inmaculada, Guardia, Marcel, Pelinovsky, Dmitry E.
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematical Physics Mathematics - Analysis of PDEs Nonlinear Sciences - Pattern Formation and Solitons
Druh dokumentu:	Working Paper
Popis:	Exponential small splitting of separatrices in the singular perturbation theory leads generally to nonvanishing oscillations near a saddle--center point and to nonexistence of a true homoclinic orbit. It was conjectured long ago that the oscillations may vanish at a countable set of small parameter values if there exist a quadruplet of singularities in the complex analytic extension of the limiting homoclinic orbit. The present paper gives a rigorous proof of this conjecture for a particular fourth-order equation relevant to the traveling wave reduction of the modified Korteweg--de Vries equation with the fifth-order dispersion term. Comment: 66 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.01563 Zobrazit plný text záznamu View this record from Arxiv