General variable separation solution and new localized excitations for the (2 + 1)-dimensional nonlinear Schrödinger equation

Authors: Bai, Cheng L.i.n.; Hu, Hai Q.u.a.n.; Wang, Wen J.u.n.; Zhao, Hong

Source: Canadian Journal of Physics, Volume 84, Number 12, December 2006 , pp. 1107-1123(17)

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Abstract:

By applying a special Bäcklund transformation, a general variable separation solution for the (2 + 1)-dimensional nonlinear Schrödinger equation is derived. In addition to some types of the usual localized excitations, such as dromions, lumps, ring solitons, oscillated dromions, and breathers, soliton structures can be easily constructed by selecting arbitrary functions appropriately. A new class of localized excitations, like fractal-dromions, fractal-lumps, peakons, compactons, and folded excitations of this system is found by selecting appropriate functions. Some interesting novel features of these structures are revealed.PACS Nos.: 05.45.-a, 02.30.Jr

Suite à une transformation spéciale de Bäcklund, nous obtenons une solution générale en séparation de variables pour l'équation non linéaire de Schrödinger. En plus de types habituels d'excitations comme les dromions, les bosses, les solitons en anneau, les dromions oscillants et les gonflements quantiques (breathers), des structures solitoniques peuvent facilement être construites en sélectionnant des fonctions arbitraires de façon appropriée. Nous trouvons une nouvelle classe d'excitations localisées, comme le dromion fractal, la bosse fractale, les picons, les compactons et les excitations repliées de ce système en sélectionnant les fonctions appropriées. Nous soulignons certaines caractéristiques nouvelles de ces structures.[Traduit par la Rédaction]

Document Type: Research article

Publication date: 2006-12-01

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General variable separation solution and new localized excitations for the (2 + 1)-dimensional nonlinear Schrödinger equation

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