相关论文: Existence and asymptotic behavior of solutions for…

The sine-Gordon equation is a nonlinear partial differential equation. It is known that the sine-Gordon has soliton solutions in the 1D and 2D cases, but such solutions are not known to exist in the 3D case. Several numerical solutions to…

We consider the Cauchy problem of coupled 3-D wave and Klein-Gordon equations with a quadratic form of nonlinearity. We show global existence under several conditions, including large derivative data for wave equations and the null…

On the three dimensional Euclidean space, for data with finite energy, it is well-known that the Maxwell-Klein-Gordon equations admit global solutions. However, the asymptotic behaviours of the solutions for the data with non-vanishing…

We describe completely 2-solitary waves related to the ground state of the nonlinear damped Klein-Gordon equation \begin{equation*} \partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \end{equation*} on $\bf R^N$, for $1\leq N\leq…

In this article we will develop some techniques aimed at the strong couplings in two-dimensional wave-Klein-Gordon system. We distinguish the roles of different type of decay factors and develop a method which permits us to "exchange" one…

We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, R. Xue (2004), we show the…

Focusing on multi-solitons for the Klein-Gordon equations, in first part of this paper, we establish their conditional asymptotic stability. In the second part of this paper, we classify pure multi-solitons which are solutions converging to…

This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations with Dirichlet boundary conditions. The equations model Micro-Electro-Mechanical Systems (MEMS) and are depending on a…

We obtain sharp decay estimates and asymptotics for small solutions to the one-dimensional Klein-Gordon equation with constant coefficient cubic and spatially localized, variable coefficient cubic nonlinearities. Vector-field techniques to…

This work studies the dynamics of solutions to the sine-Gordon equation posed on a tadpole graph $G$ and endowed with boundary conditions at the vertex of $\delta$-type. The latter generalize conditions of Neumann-Kirchhoff type. The…

This paper is devoted to study the dispersive properties of the linear Klein-Gordon and wave equations on a class of locally symmetric spaces. As a consequence, we obtain the Strichartz estimate and prove global well-posedness results for…

We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the Linear Delta Expansion. All the results obtained in this article are fully…

This paper approaches the question of existence and uniqueness of stationary solutions to a semilinear hyperbolic-parabolic system and the study of the asymptotic behaviour of global solutions. The system is a model for some biological…

Under a mild Lipschitz condition we prove a theorem on the existence and uniqueness of global solutions to delay fractional differential equations. Then, we establish a result on the exponential boundedness for these solutions.

We consider for the first time the solutions of Klein-Gordon equation in gravitational field of {\em a massive} point source in GR. We examine numerically the basic bounded quantum state and the next few states in the discrete spectrum for…

We consider Maxwell-Lorentz dynamics: that is to say, Newton's law under the action of a Lorentz's force which obeys the Maxwell equations. A natural class of solutions are those given by the Lagrangian submanifolds of the phase space when…

In this paper, we study the long-time dynamics and stability properties of the sine-Gordon equation $$f_{tt}-f_{xx}+\sin f=0.$$ Firstly, we use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics…

We consider the exterior Dirichlet problem for Monge-Amp\`ere equation with prescribed asymptotic behavior. Based on earlier work by Caffarelli and the first named author, we complete the characterization of the existence and nonexistence…

Nonexistence of global weak solutions of Klein-Gordon equations with gauge variant semilinear terms are considered in Friedmann-Lema\^itre-Robertson-Walker spacetimes. Effects of spatial expansion or contraction on the solutions are studied…

We conduct a comprehensive analysis of the large-space and long-time asymptotics of kink-soliton gases in the sine-Gordon (sG) equation, addressing an important open problem highlighted in the recent work [Phys. Rev. E 109 (2024) 061001].…