Methods of Finding of Exact Analytical Solutions of Nonautonomous Nonlinear Klein-Fock-Gordon Equation

2019 ◽  
pp. 147-161 ◽  
Author(s):  
A. N. Bulygin ◽  
Yu. V. Pavlov
Keyword(s):  
Analytical Solutions ◽  
Gordon Equation ◽  
Exact Analytical Solutions

scholarly journals THE NONLINEAR AND NONLOCAL INTEGRABLE SINE‐GORDON EQUATION

2005 ◽  
Vol 10 (4) ◽  
pp. 367-376 ◽  
Author(s):  
P. Miškinis
Keyword(s):  
Analytical Solutions ◽  
Gordon Equation ◽  
Classical Solutions ◽  
Sine Gordon Equation ◽  
Exact Analytical Solutions ◽  
New Type ◽  
Interaction Term ◽  
Nonlocal Deformation

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.

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