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Paulius Miškinis - One of the best experts on this subject based on the ideXlab platform.

  • The nonlinear and nonlocal integrable sine‐Gordon Equation
    Mathematical Modelling and Analysis, 2010
    Co-Authors: Paulius Miškinis
    Abstract:

    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.

  • THE NONLINEAR AND NONLOCAL INTEGRABLE SINE‐Gordon Equation
    Mathematical Modelling and Analysis, 2005
    Co-Authors: Paulius Miškinis
    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.

P. Carbonaro - One of the best experts on this subject based on the ideXlab platform.

Chi-kun Lin - One of the best experts on this subject based on the ideXlab platform.

  • Singular Limits of the Klein–Gordon Equation
    Archive for Rational Mechanics and Analysis, 2010
    Co-Authors: Chi-kun Lin
    Abstract:

    We establish the singular limits, including semiclassical, nonrelativistic and nonrelativistic-semiclassical limits, of the Cauchy problem for the modulated defocusing nonlinear Klein–Gordon Equation. For the semiclassical limit, \({\hbar\to 0}\), we show that the limit wave function of the modulated defocusing cubic nonlinear Klein–Gordon Equation solves the relativistic wave map and the associated phase function satisfies a linear relativistic wave Equation. The nonrelativistic limit, c → ∞, of the modulated defocusing nonlinear Klein–Gordon Equation is the defocusing nonlinear Schrodinger Equation. The nonrelativistic-semiclassical limit, \({\hbar\to 0, c=\hbar^{-\alpha}\to \infty}\) for some α > 0, of the modulated defocusing cubic nonlinear Klein–Gordon Equation is the classical wave map for the limit wave function and a typical linear wave Equation for the associated phase function.

Lu Trong Khiem Nguyen - One of the best experts on this subject based on the ideXlab platform.

Christoph H Keitel - One of the best experts on this subject based on the ideXlab platform.

  • a real space split operator method for the klein Gordon Equation
    Journal of Computational Physics, 2009
    Co-Authors: Heiko Bauke, Christoph H Keitel
    Abstract:

    The Klein-Gordon Equation is a Lorentz invariant Equation of motion for spinless particles. We propose a real space split operator method for the solution of the time-dependent Klein-Gordon Equation with arbitrary electromagnetic fields. Split operator methods for the Schrodinger Equation and the Dirac Equation typically operate alternately in real space and momentum space and, therefore, require the computation of a Fourier transform in each time step. However, the fact that the kinetic energy operator [email protected]^ in the two-component representation of the Klein-Gordon Equation is a nilpotent operator, that is [email protected]^^2=0, allows us to implement the split operator method for the Klein-Gordon Equation entirely in real space. Consequently, the split operator method for the Klein-Gordon Equation does not require the computation of a Fourier transform and may be parallelized efficiently by domain decomposition.