相关论文: Symplectic transversality and the Pego-Weinstein t…
We consider quasilinear generalizations of the Korteweg-de Vries equation and dispersive perturbations of the Euler equations for compressible fluids, either in Lagrangian or in Eulerian coordinates. In particular, our framework includes…
The problem of linear instability of a nonlinear traveling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is…
For the nonlinear Dirac equation with scalar self-interaction (the Soler model) in three spatial dimensions, we consider the linearization at solitary wave solutions and find the invariant spaces which correspond to different spherical…
In this paper, we investigate the spectral stability of periodic traveling waves in the two dimensional gravity-capillary water wave problem. We derive a stability criterion based on an index function, whose sign determines the spectral…
A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=\rho$. A wide class of self-similar solutions turn…
We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of $N$ incoherently coupled nonlinear Schrodinger equations. Soliton stability is studied as a constrained…
This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…
In this paper, it is proved that the KdV-Burgers equation with a monostable source term of Fisher-KPP type has small-amplitude periodic traveling wave solutions with finite fundamental period. These solutions emerge from a subcritical local…
The Degasperis-Procesi equation is an approximating model of shallow-water wave propagating mainly in one direction to the Euler equations. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of {\it…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model…
In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work \cite{carles}, in which the authors established the well-posedness and…
A stability criterion is derived for self-similar solutions with perfect fluids which obey the equation of state $P=k\rho$ in general relativity. A wide class of self-similar solutions turn out to be unstable against the so-called kink…
Dispersive PDEs are important both in applications (wave phenomena e.g. in hy- drodynamics, nonlinear optics, plasma physics, Bose-Einstein condensates,...) and a mathematically very challenging class of partial differential equations,…
Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber…
Choosing ${\kappa}$ (horizontal ordinate of the saddle point associated to the homoclinic orbit) as bifurcation parameter, bifurcations of the travelling wave solutions is studied in a perturbed $(1 + 1)$-dimensional dispersive long wave…
The paper is devoted to numerical study of stability of nonlinear localized modes ("gap solitons") for the spatially one-dimensional Gross-Pitaevskii equation (1D GPE) with periodic potential and repulsive interparticle interactions. We use…
Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…