Related papers: Asymptotic two-soliton solutions in the Fermi-Past…
The Fermi-Pasta-Ulam (FPU) lattice with periodic boundary conditions and $n$ particles admits a large group of discrete symmetries. The fixed point sets of these symmetries naturally form invariant symplectic manifolds that are investigated…
We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general…
Solitons in one-dimensional parity-time (PT)-symmetric periodic potentials are studied using exponential asymptotics. The new feature of this exponential asymptotics is that, unlike conservative periodic potentials, the inner and outer…
We consider persistence properties of solutions for a generalised wave equation including vibration in elastic rods and shallow water models, such as the BBM, the Dai's, the Camassa-Holm, and the Dullin-Gottwald-Holm equations, as well as…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we solve in the asymptotic long-time regime the master equation for two independent harmonic oscillators interacting with an…
We give a complete study of the asymptotic behavior of a simple model of alignment of unit vectors, both at the level of particles , which corresponds to a system of coupled differential equations, and at the continuum level, under the form…
The spatiotemporal propagation behavior of a solitary wave is investigated on a Fermi-Pasta-Ulam ring. We observe the emergence of a cnoidal wave excited by the solitary wave. The cnoidal wave may coexist with the solitary wave for a long…
In this study, we consider the following extended attraction chemotaxis system of two species parabolic-parabolic-elliptic type with nonlocal terms \[ \begin{cases} u_t=d_1\Delta u-\chi_1\nabla (u\cdot \nabla…
We consider the one-dimensional nonlinear Schr\"odinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and…
We consider the quadratic Zakharov-Kuznetsov equation $$ \partial_t u + \partial_x \Delta u + \partial_x u^2 =0 $$ on $\mathbb{R}^3$. A solitary wave solution is given by $Q(x-t,y,z)$, where $Q$ is the ground state solution to $-Q + \Delta…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
We show that for non-negative solution of the Aronsson equation an isolated singularity is either removable, or the solution behaves asymptotically like a general cone. This generalizes the asymptotic behavior theory for infinity harmonic…
We introduce a generalized $d$-dimensional Fermi-Pasta-Ulam (FPU) model in presence of long-range interactions, and perform a first-principle study of its chaos for $d=1,2,3$ through large-scale numerical simulations. The nonlinear…
The asymptotic study of a time-dependent function $f$ as the solution of a differential equation often leads to the question of whether its derivative $\dot f$ vanishes at infinity. We show that a necessary and sufficient condition for this…
We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally…
We consider the V-A Fermi interaction and apply an earlier developed method for summing up the leading asymptotics for scattering amplitudes in non-renormalizable theories. We consider the amplitude of fermion-antifermion scattering and…
We investigate the asymptotic behavior, as t goes to infinity, for a semilinear hyperbolic equation with asymptotically smal dissipation and convex potential. We prove that if the damping term behaves like K/t^\alpha for t large enough, k>0…
We consider the Hartree and Schr\"{o}dinger equations describing the time evolution of wave functions of infinitely many interacting fermions in three-dimensional space. These equations can be formulated using density operators, and they…
We consider singularly perturbed second order elliptic system in the whole space with fast oscillating coefficients. We construct the complete asymptotic expansions for the eigenvalues converging to the isolated ones of the homogenized…
We examine a collection of particles interacting with inverse-square two-body potentials in the thermodynamic limit. We find explicit large-amplitude density waves and soliton solutions for the motion of the system. Waves can be constructed…