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The nonlinear and nonlocal integrable sine‐Gordon equation

    P. Miškinis Affiliation

Abstract


A new type of the nonlocal sine‐Gordon equation with the generalized interaction term is suggested. Its limit cases, symmetries and exact analytical solutions are obtained. This type of the nonlocal sine‐Gordon equation is shown to possess one‐, two‐ and N‐solitonic solutions which are a nonlocal deformation of the corresponding classical solutions of the sine‐Gordon equation.



Pasiūlyta nauja nelokali sine‐Gordono evoliucine lygtis su apibendrintu saveikos nariu. Nustatyti šios lygties ribiniai atvejai, Lagranžianas, simetrijos, tikslūs analiziniai sprendiniai. Parodyta, kad šios rūšies nelokali sine‐Gordono lygtis turi vieno, dvieju bei N‐solitoninius sprendinius, kurie yra atitinkamu klasikiniu sine‐Gordono lygties sprendiniu nelokalios deformacijos. Nelokalios sine‐Gordono lygties integruojamumas siejamas su geometrinemis dvimačiu nelokaliai deformuotu paviršiu savybemis.


First Published Online: 14 Oct 2010

Keyword : nonlocality, SG equation, integrability

How to Cite
Miškinis, P. (2005). The nonlinear and nonlocal integrable sine‐Gordon equation. Mathematical Modelling and Analysis, 10(4), 367-376. https://doi.org/10.3846/13926292.2005.9637294
Published in Issue
Dec 31, 2005
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