Breather solution of non-linear Klein-Gordon equation
D. V. Zav'yalov, V. I. Konchenkov, S. V. Kryuchkov
本研究提出获取Klein-Gordon方程近似呼吸子解的技术，探究了石墨烯基超晶格中非线性波传播对应的该方程的呼吸子解。
本文提出一种获取Klein-Gordon方程近似呼吸子解的技术，研究了描述石墨烯基超晶格中非线性波传播的该方程的呼吸子解。
A technique for obtaining an approximate breather solution of the Klein-Gordon equation is presented. A breather solution of the equation describing the propagation of nonlinear waves in a graphene-based superlattice is investigated.
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The noncommutative sine-Gordon breather
如[hep-th/0406065]中所示，sine-Gordon模型存在非对易变形，其保持（经典）可积，但具有第二个标量场。我们采用敷料方法（适用于Moyal变形的情况）来构造变形的扭结-抗扭结和通气构型。显式的结果和绘图的领先的非交换性修正呼吸。其时间周期性不变。
We prove the existence of time-periodic solutions and spatially localised solutions (breathers), in general nonlinear Klein-Gordon infinite lattices. The existence problem is converted into a fixed point problem for an operator on some appropriate function space which is solved by means of Schauder's Fixed Point Theorem.
Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations
本文证明了离散Klein-Gordon方程中具有小耦合常数的多点呼吸子谱稳定性的最一般定理。在反连续极限中，多位点呼吸子代表在由多个“空穴”（静止位点）分隔的晶格的不同位点处的激发振荡。该定理描述了多点呼吸子的稳定性或不稳定性如何取决于受激振子之间的相位差和距离。以前，只有多站点呼吸相邻激发站点被认为是在一阶微扰理论。我们发现，多位呼吸子与一个位置的孔的稳定性变化的大振幅振荡软非线性势。我们还发现并研究了软四次势中1：3共振点附近的单点和多点呼吸子的分叉现象。
Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For nonlinear Klein-Gordon equations, their breather solutions are usually known as time periodic solutions with the vanishing spatial-boundary condition. The existence of breather solution is known for the Sine-Gordon equations, while the Sine-Gordon equations are also known as the soliton equation. The breather solutions is a certain kind of time periodic solutions that are not only play an essential role in the bridging path to the chaotic dynamics, but provide multi-dimensional closed loops inside phase s…
Breathers in the elliptic sine-Gordon model
本文给出了椭圆sine-Gordon模型中孤子-反孤子扇区中散射振幅的新表达式，该表达式用仿射Weyl群的陪集表示，对应于q-变形Gamma函数的无穷乘积.当放松对耦合常数的通常限制时，该模型包含额外的束缚态，可以将其解释为呼吸子。这些呼吸束缚态必然伴随着超光速粒子。我们计算了描述呼吸子相互散射和与孤子-反孤子扇区散射的完整S矩阵。我们进行各种减少的模型，其中之一导致一种新的理论，即椭圆形版本的最小D（n+1）-仿射户田场论。
Wedge-local observables in the deformed sine-Gordon model
在（1+1）维Minkowski空间的可积量子场论的Bootstrap方法中，我们构造了两粒子S-矩阵，并试图研究局域观测量。证明了无质量sine-Gordon模型与Thirring模型是等价的，并且它的呼吸子-呼吸子S矩阵分量（其中第一个呼吸子对应于sine-Gordon模型的标量场）在融合下是闭合的.然而，这个呼吸子-呼吸子S-矩阵的极点的留数有错误的符号，不能被认为是一个单独的模型。我们发现CDD因素调整的迹象，使呼吸者呼吸S-矩阵单独满足合理的假设。然后，我们提出了候选人的观察楔形区域，并证明其交换性在弱意义上。
In this paper we consider a discrete Klein-Gordon (dKG) equation on $\ZZ^d$ in the limit of the discrete nonlinear Schrodinger (dNLS) equation, for which small-amplitude breathers have precise scaling with respect to the small coupling strength $\eps$. By using the classical Lyapunov-Schmidt method, we show existence and linear stability of the KG breather from existence and linear stability of the corresponding dNLS soliton. Nonlinear stability, for an exponentially long time scale of the order $\mathcal{O}(\exp(\eps^{-1}))$, is also obtained via the normal form technique, together with highe…
Breather-like structures in modified sine-Gordon models
我们报告了在（1+1）维可积sine-Gordon模型的变形理论中，呼吸者型场组态的分析和数值结果。我们的研究的主要动机是测试背后的想法最近提出的准可积性的概念，这是从观察到，一些场论提出了无限数量的数量是渐近守恒的散射的孤子，和周期性的情况下，呼吸器的配置。尽管造成这种现象的机制还没有被很好地理解，但很明显，时空宇称变换下解的特殊性质起着至关重要的作用。本文的数值结果支持了准可积性的观点，并发现极长寿命呼吸组态满足这些宇称性质。我们还报告了一种机制，特别是在这里研究的理论，有利于长期存在的呼吸，即使在显着变形的正弦戈登潜在的情况下。
N=1 super sinh-Gordon model in the half line: Breather solutions
我们研究了N=1的超sinh-Gordon（SShG）模型限制到半线通过减少从缺陷SShG模型。利用贝克隆变换得到了该模型的单孤子、双孤子和三孤子解以及一类呼吸子解。这样的经典解决方案的参数满足一定的约束，以保持可积性和超对称性的原始体理论。此外，当执行纯玻色子极限时，以前的结果被恢复。
The quantum sine-Gordon model is the simplest massive interacting integrable quantum field theory whose two-particle scattering matrix is generally non-diagonal. As such, it is a model that has been extensively studied, especially in the context of the bootstrap programme. In this paper we compute the form factors of a special local field known as the branch point twist field, whose correlation functions are building blocks for measures of entanglement. We consider the attractive regime where the theory posesses a particle spectrum consisting of a soliton, an antisoliton (of opposite $U(1)$ ch…
In this report, the various 1D single soliton and multi-soliton solutions of the Sine-Gordon equation are explored. First the topological kink solitons and their properties for the Sine-Gordon, as well as the $ϕ^{4}$ model are investigated. This includes energy and momentum conservation laws for both models, as well as static kinks and antikinks. The Bogomol'nyi equation and the importance of Lorentz invariance are also discussed. Then in the second half, the focus is on Sine-Gordon multi-kink solutions, which are found by a separation of variables method rather than using inverse scattering o…
Dimensional deformation of sine-Gordon breathers into oscillons
本文通过将 sine-Gordon 模型维度作为实参数形变呼吸子，生成球对称振荡子，发现小形变下振荡子可视为微扰呼吸子，并在高维中观察到核心间歇收缩膨胀及临界动力学。
The Cauchy Problem for Non-Archimedean Pseudodifferential Equations of Klein-Gordon Type
本文引入了一类新的Klein-Gordon型非阿基米德拟微分方程，并研究了这类方程的Cauchy问题.一个值得注意的事实是，非阿基米德Klein-Gordon方程表现出许多类似于经典Klein-Gordon方程的性质。
Nonexistence of small, odd breathers for a class of nonlinear wave equations
本文证明了对于一类具有奇非线性项的非线性波动方程，任何在能量空间中很小的整体奇解在局部能量范数下衰减到$0$.特别地，这个结果表明了一些经典的非线性Klein Gordon方程如sine Gordon方程和$ϕ^4$和$ϕ^6$模型不存在小的奇呼吸子.它也部分地回答了Soffer和Weinstein在\cite [p.19]{MR 1681113}中提出的关于一维立方NLKG呼吸子不存在的问题。
On Dispersive Decay for Discrete 3D Schrödinger and Klein-Gordon Equations
我们推导出离散三维薛定谔方程和克莱因-戈登方程的解的加权范数的长时间衰减。
We give estimates for the changes of the eigenvalues of the Klein Gordon operator under the change of the potential. In some relevant situations we improve the existing estimates. We test our results on some exactly solvable models (Coulomb potential, Klein-Gordon oscillator).
Breaking integrability at the boundary: the sine-Gordon model with Robin boundary conditions
我们探讨边界散射的正弦戈登模型与不可积家庭的罗宾边界条件。碰撞后的领域的孤子内容进行了分析，使用与逆散射方法的直接散射问题的数值实现。我们发现，antikink可以反映到各种组合的antikink，扭结，和一个或多个呼吸器，取决于初始antikink速度和与边界条件相关联的参数的值。此外，我们观察到一个复杂的共振结构所产生的中间呼吸，其与边界的administration是高度依赖于呼吸阶段的创建区域。
Numerical solutions of the coupled nonlinear Klein--Gordon equations by trigonometric integrator pseudospectral discretization
本文提出了一种基于三角多项式的时间积分器的空间导数伪谱近似方法，用于求解耦合非线性Klein-Gordon方程。对一耦合和三耦合的Klein-Gordon方程进行了数值试验，旨在了解其精度和稳定性，并展示其在应用中的效率和高分辨率能力。
We introduce $q$-versions of the Klein-Gordon equation in the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to our $q$-deformed Klein-Gordon equations. We show that these plane wave solutions form a complete orthogonal system. We discuss the propagators of our $q$-deformed Klein-Gordon equations. We derive continuity equations for the charge density, the energy density, and the momentum density of a $q$-deformed spin-zero particle.
Superoscillations and the Klein-Gordon equation via the Fourier method
本文通过傅里叶方法，研究以超振荡为初始数据的Klein-Gordon方程时间演化问题，并利用Segal-Bargmann变换推导出解的积分表示。
Scattering problem for Klein-Gordon equation with cubic convolution nonlinearity
研究了具有立方卷积非线性项的Klein-Gordon方程的散射问题。基于非齐次Klein-Gordon方程的Schmidhartz估计，我们证明了散射算子的存在性.
Casimir Effect Associated with Fractional Klein-Gordon Field
本文简要回顾了近年来有关分数克莱因-戈登场的工作，特别是在各种几何形状和边界条件下与分数克莱因-戈登场相关的卡西米尔效应。给出了分数阶Klein-Gordon质量场引起的Casimir活塞的新结果。
The Klein-Gordon equation with a generalized Hulthen potential in D-dimensions
在离心项近似的框架下，得到了$D$维中一般Hulthén型势的Klein-Gordon方程的近似解.用超几何多项式的形式得到了束缚态能量本征值和归一化本征函数。
We show decay of the local energy of solutions of the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordström spacetime by means of a resonance expansion of the local propagator.
Klein-Gordon equations with homogeneous time-dependent electric fields
我们考虑了一个与Klein-Gordon方程相关的系统，该系统具有含时均匀电场。Veselić在1991年证明了这个系统的时间演化传播子的上、下界，其中电场与时间无关。我们将这个结果推广到含时电场。
Exact Solutions of the Klein-Gordon Equation with Hylleraas Potential
本文用Nikiforov-Uvarov方法给出了具有Hylleraas势的Klein-Gordon方程的精确解。我们明确地得到了束缚态能量本征值和相应的本征函数，并用雅可比多项式表示
Interplay between Dynamic Systems Described by the Klein-Gordon and Dirac Equations
结果表明，在二维时空中，只要适当地重新定义电流和能量动量张量，由自由Klein-Gordon方程描述的动力学系统就转化为由自由Dirac方程描述的动力学系统.
The scalar Klein-Gordon equation describes wave motion in a waveguide with a cut-off. For example, the displacement of an elastic cord anchored to a solid base by elastic elements can be described by the scalar Klein-Gordon equation. We analyse this equation using the concept of analytical continuation of dispersion diagram. Particularly, it is shown that the dispersion diagram is topologically equivalent to a tube analytically embedded in two-dimensional complex space. The corresponding Fourier integral is studied on this tube using the Cauchy's theorem. The basic properties of the scalar Kle…
On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory
椭圆伪解析函数理论在几十年前由Bers和Vekua独立考虑。本文利用双曲数代数发展了伪解析函数论的双曲类比。我们考虑带位势的Klein-Gordon方程。借助于一个特殊的解决方案，我们因式分解的Klein-Gordon算子的两个Vekua型运营商。我们表明，这些Vekua型运营商之一的解决方案的实部所考虑的克莱因-戈登方程的解决方案。利用双曲伪解析函数理论，我们得到显式构造的无限系统的解决方案的Klein-Gordon方程的潜力。最后，我们给出了所提出的程序的应用程序的一些例子。
On long-time decay for modified Klein-Gordon equation
我们得到了运动标架中Klein-Gordon方程解的加权能量范数的色散长时间衰减。这种衰变推广了Jensen，Kato和Murata关于薛定谔型方程的结果。我们修改的方法，使其适用于相对论方程。
Resonant pumping in nonlinear Klein-Gordon equation and solitary packets of waves
研究了受小外力扰动的非线性Klein-Gordon方程的解.扰动的频率变化缓慢，并通过共振。共振产生孤立波包。完整的渐近描述这个过程。
We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing the standard partial derivatives by the Dunkl derivatives in the standard Klein--Gordon (KG) equation. We show that the generalization with Dunkl derivative of the $z$-component of the angular momentum is what allows the separation of variables of the DKG equation. Then, we compute the energy spectrum and eigenfunctions of the DKG equations for the 2D Coulomb potential and the Klein--Gordon oscillator analytically and from an ${\rm su}(1,1)$ algebraic point of view. Finally, we show that if the parameters of the Dunkl deriv…
A Remark on Long Range Scattering for the nonlinear Klein-Gordon equation
考虑一维空间中长程临界非线性Klein-Gordon散射问题。
Equivalence of the Klein-Gordon random field and the complex Klein-Gordon quantum field
描述了Klein-Gordon随机场和复Klein-Gordon量子场之间的差异，明确比较了两种理论中测试函数的负频率模式在产生和湮灭算符表述中所起的作用.随机场和复量子场都可以由相同的创造和湮灭算子代数构造，使它们在这个意义上是等价的。
Ground state solutions for the nonlinear Klein-Gordon-Maxwell equations
本文证明了静电场情形下非线性Klein-Gordon-Maxwell方程基态解的存在性。
Existence of hylomorphic solitary waves in Klein-Gordon and in Klein-Gordon-Maxwell equations
粗略地说，孤波是场方程的解，其能量作为局部化的包传播，并且在时间上保持这种局部化。具有不为零的角动量的孤波称为涡旋。我们知道（至少）三种可能产生孤波和涡旋的机制：1）完全可积性（如Kortewg-de Vries方程）; 2）拓扑约束（如Sine-Gordon方程）; 3）能荷比（如非线性Klein-Gordon方程）。第三种类型的孤波或孤波称为半纯波。这一类包括Q球，它是非线性Klein-Gordon方程（NKG）的球对称解，以及孤波和涡旋，它们以相同的机制出现在非线性薛定谔方程和规范理论中。本文给出了一个抽象定理，证明了非线性Klein-Gordon-Maxwell方程（NKGM）和非线性Klein-Gordon-Maxwell方程（NKGM）中半纯孤波、孤子和涡旋的存在性
We show asymptotic completeness for the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordström spacetime when the product of the charge of the black hole with the charge of Klein-Gordon field is small enough. We then interpret scattering as asymptotic transports along principal null geodesics in a Kaluza-Klein extension of the original spacetime.
On the Klein-Gordon oscillator subject to a Coulomb-type potential
通过在Klein-Gordon方程的质量项中引入标量势，研究了库仑型势对Klein-Gordon振子的影响.相对论束缚态的解决方案，实现了吸引和排斥库仑型势和产生的量子效应的特点是依赖于系统的量子数的Klein-Gordon振荡器的角频率。
Exact solution of the Klein Gordon equation in the presence of a minimal length
在存在极小长度的条件下，得到了具有线性向量势和标量势的（1+1）维KleinGordon方程的精确解.本文还研究了该问题的代数方法。
Shape invariance approach to exact solutions of the Klein-Gordon equation
利用形状不变性，我们得到了（1+1）维Klein-Gordon方程在某些类型的标量势和矢量势下的精确解.我们还讨论了在此框架下获得非厄米相互作用实能谱的可能性。
We are interested in the Klein-Gordon-Zakharov equations in $\mathbb{R}^{1+3}$, and we aim to show that the energy for the global solution to the equations is uniformly bounded, and we do not require the compactness assumption on the initial data. To achieve these goals, the key is to apply Alinhac's ghost weight energy estimates adapted to the Klein-Gordon equations.
We describe a Lorentzian manifold that is globally hyperbolic and geodesically complete, but such that the (minimally coupled) Klein-Gordon operator with the standard domain is not essentially self-adjoint.
Consider the Klein-Gordon-Zakharov equations in $\mathbb{R}^{1+2}$, and we are interested in establishing the small global solution to the equations and in investigating the pointwise asymptotic behavior of the solution. The Klein-Gordon-Zakharov equations can be regarded as a coupled semilinear wave and Klein-Gordon system with quadratic nonlinearities which do not satisfy the null conditions, and the fact that wave components and Klein-Gordon components do not decay sufficiently fast makes it harder to conduct the analysis. In order to conquer the difficulties, we will rely on the hyperboloi…
Perturbed Coulombic potentials in Dirac and Klein-Gordon equations
我们的伪移位$\ell$ -展开技术的相对论性扩展，提出了解决的Dirac和Klein-Gordon方程的本征值。再次，我们通过与现有的数值积分数据的比较，显示其结果的数值有用性。
Modified Klein-Gordon-Fock equations based on one-dimensional chaotic dynamics and groups with broken symmetry
在一维混沌动力学的基础上得到了修正的Klein-Gordon-Fock方程。引入了\textit{m} -指数映射和对称性破缺群的概念。本文研究了一个二元正交函数系。
Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption
我们将我们以前的结果在三维聚焦立方Klein-Gordon方程的非径向的情况下，给出了一个完整的分类的全球动力学的所有解决方案的能量至多略高于基态。
A Nekhoroshev type theorem for the nonlinear Klein-Gordon equation with potential
研究了一维非线性带卷积势的Klein-Gordon（NLKG）方程，证明了具有小解析范数的解在指数长时间内保持小解.该结果相对于$c \geq 1$是一致的，然而它必须属于一个大测度集。
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.
Asymptotic completeness for superradiant Klein-Gordon equations and applications to the De Sitter Kerr metric
证明了一类超辐射Klein-Gordon方程的渐近完备性。我们的结果被应用到Klein-Gordon方程的De Sitter Kerr度规与小角动量的黑洞。对于这个方程，我们得到了场的固定角动量的渐近完备性。
The Klein-Gordon operator on Möbius strip domains and the Klein bottle in $\mathbb{R}^n$
本文给出了Klein-Gordon算子在Möbius带和Klein瓶的某些高维推广上的基本解的显式公式，其值在不同的pinor丛中.的基本解决方案中描述的Weierstraffield $\wp$ -功能，适应这些几何形状的上下文中的概括。显式公式的内核，然后让我们来表达所有的解决方案的齐次和非齐次克莱因-戈登问题与给定的边界数据在这些流形的背景下。在克莱因瓶的情况下，我们能够描述所有的零解的克莱因-戈登方程的基本解及其偏导数的有限线性组合。
We report on the well-posedness of the Feynman problem for the Klein-Gordon equation on asymptotically Minkowski spacetimes. The main result is the invertibility of the Klein-Gordon operator with Feynman conditions at infinite times. Furthermore, the inverse is shown to coincide with the Duistermaat-Hörmander Feynman parametrix modulo smoothing terms.
Localized Solutions of the Non-Linear Klein-Gordon Equation in Many Dimensions
本文给出了多空间变量非线性Klein-Gordon方程的一个新的复非定常类粒子解。该结构是基于减少到一个常微分方程。
Smooth Solutions and Discrete Imaginary Mass of the Klein-Gordon Equation in the de Sitter Background
利用半单李代数理论中的方法，我们可以得到4维德西特时空（dS ^[4]）上克莱因-戈登方程的所有光滑解。dS ^4上的克莱因-戈登标量的质量与so（1，4）的卡西米尔算子的本征值有关。因此，它是离散的，或量化的。此外，dS^4上的克莱因-戈登标量的质量m是虚数：m^2与-N（N+3）成比例，其中N >= 0是整数。
We consider the stability of the toroidal AdS-Schwarzshild black holes as solutions of the Einstein--Klein-Gordon system, with Dirichlet or Neumann boundary conditions for the scalar field. Restricting to perturbations that respect the toroidal symmetry we show both orbital and asymptotic stability for the full nonlinear problem, for a range of choices of the Klein-Gordon mass. The solutions we construct with Neumann boundary conditions have a Hawking mass which diverges towards infinity, reflecting the infinite energy of the Klein-Gordon field for perturbations satisfying these boundary condi…
Time-Periodic Einstein--Klein--Gordon Bifurcations of Kerr
我们构造一个参数家庭的解决方案的Einstein-Klein-Gordon方程分叉的克尔解决方案，这样的基本家庭的时空是每个渐近平坦的，静止的，轴对称的，黑洞时空，并使相应的标量场是非零的和时间周期的。一个直接的推论是，对于这些克莱因-戈登质量，克尔家族作为爱因斯坦-克莱因-戈登方程的解是不渐近稳定的。
We prove that finite energy solutions to the nonlinear Schroedinger equation and nonlinear Klein--Gordon equation which have the compact time spectrum have to be one-frequency solitary waves. The argument is based on the generalization of the Titchmarsh convolution theorem to partial convolutions.
Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology
我们给出了Klein-Gordon场的正定不变内积的一个显式构造，从而解决了Klein-Gordon场的概率解释的老问题，而不必局限于正频率解的子空间.我们的方法有一个更广泛的应用领域，并可用于获得最一般的不变内积的解空间上的一个广泛的类Klein-Gordon型发展方程。我们探讨其后果的解决方案的惠勒-德威特方程与FRW-大质量实标量场模型。
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