When is the energy of the 1D damped Klein-Gordon equation decaying?
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Annalen"
DOI: 10.1007/s00208-018-1725-5
Abstract: We study time decay of the energy for the one dimensional damped Klein-Gordon equation. We give an explicit necessary and sufficient condition on the continuous damping function $$\gamma \ge 0$$γ≥0 for which the energy $$\begin{aligned}… read more here.
Keywords: energy; gordon equation; klein gordon; damped klein ... See more keywords
On the Asymptotic Expansion of Solutions to the Goursat Problem for the Sine-Gordon Equation
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DOI: 10.1007/s10958-017-3241-7
Abstract: We construct an expansion of a solution to the Goursat problem for the sine-Gordon equation with respect to a small parameter that is involved in the data on characteristics. We prove that the expansion obtained… read more here.
Keywords: sine gordon; expansion; problem sine; gordon equation ... See more keywords
Analytical soliton solutions of the (2$$+$$+1)-dimensional sine-Gordon equation
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DOI: 10.1007/s11071-016-3241-z
Abstract: In this letter, we investigated a new (2$$+$$+1)-dimensional sine-Gordon equation. By the subsidiary ordinary differential equation method, some new explicit solutions are given. These solutions include hyperbolic function solutions and trigonometric function solutions amongst others.… read more here.
Keywords: sine gordon; gordon equation; analytical soliton; dimensional sine ... See more keywords
A high-order nonlinear Schrödinger equation as a variational problem for the averaged Lagrangian of the nonlinear Klein–Gordon equation
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DOI: 10.1007/s11071-019-05197-x
Abstract: We use Whitham’s averaged Lagrangian method extended with the multiple-scale formalism to derive a sixth-order nonlinear Schrodinger equation for the complex amplitude of the envelope of the slowly modulated wave trains whose evolution is governed… read more here.
Keywords: nonlinear klein; gordon equation; klein gordon; equation ... See more keywords
On the two-dimensional hyperbolic stochastic sine-Gordon equation
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DOI: 10.1007/s40072-020-00165-8
Abstract: We study the two-dimensional stochastic sine-Gordon equation (SSG) in the hyperbolic setting. In particular, by introducing a suitable time-dependent renormalization for the relevant imaginary Gaussian multiplicative chaos, we prove local well-posedness of SSG for any… read more here.
Keywords: sine gordon; gordon equation; two dimensional; sine ... See more keywords
Wave dynamics on networks: Method and application to the sine-Gordon equation
Sign Up to like & getrecommendations! Published in 2018 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2018.03.010
Abstract: We consider a scalar Hamiltonian nonlinear wave equation formulated on networks; this is a non standard problem because these domains are not locally homeomorphic to any subset of the Euclidean space. More precisely, we assume… read more here.
Keywords: sine gordon; gordon equation; wave dynamics; equation ... See more keywords
The integrable time-dependent sine-Gordon equation with multiple optical kink solutions
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DOI: 10.1016/j.ijleo.2019.01.018
Abstract: Abstract In this work, we study the sine-Gordon equation with time-dependent coefficient. We show that this time-dependent equation passes the Painleve test for any analytic time-dependent coefficient. This confirms its integrability in a like manner… read more here.
Keywords: sine gordon; gordon equation; optical kink; equation ... See more keywords
Almost global existence for the semi-linear Klein–Gordon equation on the circle
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DOI: 10.1016/j.jde.2016.12.013
Abstract: Abstract We show that the solution to the semi-linear Klein–Gordon equation on the circle with a nonlinearity satisfying a convenient condition, exists almost globally, for almost every positive mass, provided that it is either even… read more here.
Keywords: gordon equation; linear klein; semi linear; klein gordon ... See more keywords
Hs-class construction of an almost invariant slow subspace for the Klein–Gordon equation in the non-relativistic limit
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DOI: 10.1063/1.5027040
Abstract: We consider the linear Klein–Gordon equation in one spatial dimension with periodic boundary conditions in the non-relativistic limit where e = ℏ2/(mc2) tends to zero. It is classical that the equation is well posed, for… read more here.
Keywords: relativistic limit; gordon equation; klein gordon; equation ... See more keywords
The Klein–Gordon equation on the hyperboloidal anti-de Sitter Schwarzschild black hole
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DOI: 10.1088/1361-6382/ab5def
Abstract: In this paper we establish energy decay for solutions to the Klein-Gordon equation on the positive mass hyperboloidal anti-de Sitter Schwarzschild black hole, subject to Dirichlet, Neumann and Robin boundary conditions at infinity, for a… read more here.
Keywords: schwarzschild black; anti sitter; sitter schwarzschild; gordon equation ... See more keywords
Bound state solutions of the hyper-radial Klein-Gordon equation under the Deng-Fan potential by WKB and SWKB methods
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DOI: 10.1088/1402-4896/ac38d4
Abstract: The energy levels of the Klein–Gordon equation in hyper-radial space under the Deng-Fan potential energy function are studied by the SWKB and WKB approximation methods. We obtained the analytic solution of the energy spectra and… read more here.
Keywords: state; energy; gordon equation; klein gordon ... See more keywords