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Computers and Mathematics with Applications, ISSN 0898-1221, 12/2019, Volume 78, Issue 12, pp. 3713 - 3730
In this study, we introduce the nonlinear variable-order time fractional two-dimensional (2D) Klein–Gordon equation by using the concept of variable-order... 
Variable-order time fractional derivatives | Stability analysis | Nonlinear 2D Klein–Gordon equation | Two-dimensional Legendre wavelets (2D LWs)
Journal Article
Acta Applicandae Mathematicae, ISSN 0167-8019, 8/2019, Volume 162, Issue 1, pp. 145 - 164
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 230, Issue 2, pp. 400 - 410
Journal Article
Communications in Theoretical Physics, ISSN 0253-6102, 2018, Volume 69, Issue 5, pp. 506 - 512
We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear... 
nonlinear Klein-Gordon equation | operational calculus | partial differential equations | CONVERGENCE | PHYSICS, MULTIDISCIPLINARY | DECOMPOSITION METHOD
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 11/2019
Journal Article
Acta Physica Polonica B, ISSN 0587-4254, 01/2009, Volume 40, Issue 1, pp. 59 - 66
We study weak solutions to the Klein-Gordon equation with the logarithmic nonlinearity on interval. Such kinds of nonlinearities appear in inflation cosmology... 
SOLITONS | PHYSICS, MULTIDISCIPLINARY | GAUSSONS | SCHRODINGER-EQUATION | MODEL | NONLINEAR-WAVE MECHANICS | QUANTUM-MECHANICS | PULSONS | SOBOLEV INEQUALITIES
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 01/2017, Volume 149, pp. 81 - 110
The Neumann initial–boundary value problem for the nonlinear Klein–Gordon equation for real , , and , is considered. We prove the global well-posedness for the... 
Neumann problem | Initial–boundary value problem | Nonlinear Klein–Gordon equation | Scattering-critical | MATHEMATICS | MATHEMATICS, APPLIED | SMALL AMPLITUDE SOLUTIONS | ONE SPACE DIMENSION | GLOBAL EXISTENCE | SYSTEMS | Initial-boundary value problem | Nonlinear Klein-Gordon equation | SCATTERING
Journal Article
Physica Scripta, ISSN 0031-8949, 09/2017, Volume 92, Issue 10, p. 105001
Many neutron star features can be accurately modeled only if one assumes that a significant portion of the neutron star interior is in a superfluid state and... 
nonlinear Klein-Gordon equation | neutron stars | relativistic superfluidity | STRINGS | VORTICES | ROTATING NEUTRON-STAR | MODELS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 11/2019, Volume 2169, Issue 1
We have discussed the quantum particle model for the case of a free particle solution in the one-dimensional Klein-Gordon nonlinear equations. This model was... 
Conservation laws | Nonlinear equations | Hamilton-Jacobi equation | Mathematical analysis | Continuity equation | Klein-Gordon equation | Quantum mechanics | Derivation | Mathematical functions | Mathematical models
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2019, Volume 268, Issue 1, pp. 353 - 388
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein–Gordon... 
Standing waves | Orbital stability | Nonlinear Klein–Gordon equation | Delta potential | MATHEMATICS | SOLITONS | SOLITARY WAVES | STRONG INSTABILITY | SCHRODINGER-EQUATION | Nonlinear Klein-Gordon equation
Journal Article
PLoS ONE, ISSN 1932-6203, 02/2018, Volume 13, Issue 2, p. e0192281
In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear... 
FERROMAGNETIC SPIN CHAIN | TRANSFORMATION | EXISTENCE | RATIONAL SOLUTIONS | MULTIDISCIPLINARY SCIENCES | BREATHERS | SOLITARY SOLUTIONS | Singularities | Partial differential equations | Optics | Waves | Optical waveguides | Information science | Mathematical analysis | Klein-Gordon equation | Schroedinger equation | Mathematical models | Solitary waves | Symmetry | Breathers
Journal Article
Physics Letters A, ISSN 0375-9601, 04/2019, Volume 383, Issue 12, pp. 1274 - 1282
We consider a damped, parametrically driven discrete nonlinear Klein–Gordon equation, that models coupled pendula and micromechanical arrays, among others. To... 
Discrete nonlinear Schrödinger equation | Discrete Klein–Gordon equation | Discrete breather | Discrete soliton | Small-amplitude approximation | WAVES | PHYSICS, MULTIDISCIPLINARY | Discrete Klein-Gordon equation | DOMAIN-WALLS | BREATHERS | LATTICES | Discrete nonlinear Schrodinger equation | Islamic schools | Analysis | Numerical analysis
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 04/2017, Volume 272, Issue 7, pp. 3019 - 3092
We consider the periodic defocusing cubic nonlinear Klein–Gordon equation in three dimensions in the symplectic phase space . This space is at the critical... 
Symplectic non-squeezing | Random initial data | Nonlinear Klein–Gordon equation
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 10/2019, Volume 98, Issue 1, pp. 359 - 374
We use Whitham’s averaged Lagrangian method extended with the multiple-scale formalism to derive a sixth-order nonlinear Schrödinger equation for the complex... 
Method of multiple scales | Nonlinear dispersion | Classical Mechanics | Quasi-soliton | Envelope | Averaged Lagrangian | Engineering | Vibration, Dynamical Systems, Control | Nonlinear Klein–Gordon equation | Sine-Gordon equation | Automotive Engineering | Mechanical Engineering | Nonlinear Schrödinger equation
Journal Article
Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 07/2017, Volume 33, Issue 4, pp. 1283 - 1304
In this article, a fourth‐order compact and conservative scheme is proposed for solving the nonlinear Klein‐Gordon equation. The equation is discretized using... 
nonlinear Klein‐Gordon equation | fourth order compact and conservative scheme | variational limit integral method | nonlinear Klein-Gordon equation | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | SOLITONS | Integrals | Energy conservation | Mathematical analysis | Klein-Gordon equation | Norms | Nonlinearity | Mathematical models | Convergence
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 11/2018, Volume 23, Issue 9, pp. 3573 - 3594
We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small analytic norm remain... 
Hamiltonian systems | Nekhoroshev theorem | Nonlinear Klein-Gordon equation | Normal forms | Long time behaviour | MATHEMATICS, APPLIED | normal forms | long time behaviour | PERTURBATIONS | nonlinear Klein-Gordon equation | GLOBAL EXISTENCE | STABILITY | BIRKHOFF NORMAL-FORM | LONG-TIME EXISTENCE
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2019, Volume 474, Issue 2, pp. 814 - 832
In this paper, we show the global well-posedness and blow-up result of the solutions with the energy below the threshold for the combined nonlinear... 
Blow up | Combined nonlinear Klein–Gordon equation | Threshold energy | MATHEMATICS | MATHEMATICS, APPLIED | DEFINED SCATTERING OPERATORS | ENERGY SCATTERING | Combined nonlinear Klein-Gordon equation
Journal Article
by Bao, WZ and Feng, Y and Yi, WF
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, ISSN 1815-2406, 11/2019, Volume 26, Issue 5, pp. 1307 - 1334
We establish error bounds of the finite difference time domain (FDTD) methods for the long time dynamics of the nonlinear Klein-Gordon equation (NKGE) with a... 
NUMERICAL-METHODS | finite difference time domain methods | GLOBAL EXISTENCE | MODEL | PHYSICS, MATHEMATICAL | long time error analysis | PSEUDOSPECTRAL METHOD | weak nonlinearity | SPACE | BOUNDARY VALUE-PROBLEMS | WAVE EQUATIONS | oscillatory nonlinear Klein-Gordon equation | Nonlinear Klein-Gordon equation | SCHRODINGER | NONRELATIVISTIC LIMIT | SCHEMES
Journal Article
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