相关论文: Simple Non Linear Klein-Gordon Equations in 2 spac…

Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The perturbation is represented by finite collections of harmonics. The frequencies of the perturbation vary slowly and pass through the…

We investigate the long time dynamics of the nonlinear Schr\"odinger equation (NLS) with combined powers on the waveguide manifold $\mathbb{R}^d\times\mathbb{T}$. Different from the previously studied NLS-models with single power on the…

We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…

This work considers two linear operators which yield wave modes that are classified as neutrally stable, yet have responses that grow or decay in time. Previously, King et al. (Phys. Rev. Fluids, 1, 2016, 073604:1-19) and Huber et al. (IMA…

We prove scattering for the radial nonlinear Klein-Gordon equation $ \partial_{tt} u - \Delta u + u = -|u|^{p-1} u $ with $5 > p >3$ and data $ (u_{0}, u_{1}) \in H^{s} \times H^{s-1} $, $ 1 > s > 1- \frac{(5-p)(p-3)}{2(p-1)(p-2)} $ if $ 4…

Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical…

Irregular compactons and peakons from some nonlinear dispersions can be regularized by another type of nonlinear dispersion, defined by a pseudo-differential operator in physical space for the Galerkin truncation preserving finite Fourier…

Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it…

We generate non-linear representations of the Lorentz Group by unitary transformation over the Lorentz generators. To do that we use deformed scale transformations by introducing momentum-depending parameters. The momentum operator…

Nonlinear Schr\"odinger (NLS) equations with focusing power nonlinearities have solitary wave solutions. The spectra of the linearized operators around these solitary waves are intimately connected to stability properties of the solitary…

We are interested in the Klein-Gordon-Zakharov system in $\mathbb{R}^{1+2}$, which is an important model in plasma physics with extensive mathematical studies. The system can be regarded as semilinear coupled wave and Klein-Gordon equations…

We consider both the defocusing and focusing cubic nonlinear Klein--Gordon equations $$ u_{tt} - \Delta u + u \pm u^3 =0 $$ in two space dimensions for real-valued initial data $u(0)\in H^1_x$ and $u_t(0)\in L^2_x$. We show that in the…

We consider the pure-power defocusing nonlinear Klein-Gordon equation, in the energy subcritical case, posed on the product space $\mathbb R^d\times \mathbb T$, where $\mathbb T$ is the one-dimensional flat torus. In this framework, we…

We propose a procedure for computing the direct scattering transform of the periodic sine-Gordon equation. This procedure, previously used within the periodic Korteweg-de Vries equation framework, is implemented for the case of the…

We consider the cubic nonlinear Schr{\"o}dinger equation on the spatial domain $\mathbb{R}\times \mathbb{T}^d$, and we perturb it with a convolution potential. Using recent techniques of Hani-Pausader-Tzvetkov-Visciglia, we prove a modified…

We are interested in solutions of the nonlinear Klein-Gordon equation (NLKG) in $\mathbb{R}^{1+d}$, $d\ge1$, which behave as a soliton or a sum of solitons in large time. In the spirit of other articles focusing on the supercritical…

We consider the scattering problem for the nonlinear Schr\"{o}dinger equation with a potential in two space dimensions. Appropriate resolvent estimates are proved and applied to estimate the operator $A(s)$ appearing in commutator…

We construct series solutions to all orders for breathers of Klein-Gordon equations, in powers of an amplitude parameter epsilon, under a sign condition on the coefficients of the expansion of the nonlinearity. All terms may be computed…

We consider two dimensional nonstationary scattering of plane waves by a NN-wedge. We prove the existence and uniqueness of a solution to the corresponding mixed problem and we give an explicit formula for the solution. Also the Limiting…

We provide the rigorous justification of the NLS approximation, in Sobolev regularity, for a class of quasilinear Hamiltonian Klein Gordon equations with quadratic nonlinearities on large one-dimensional tori $\T_L:=\mathbb{R}/(2\pi L…