Related papers: On Soliton Resolution for a Lattice
We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus $k$. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the…
The diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is an infinite chain of alternating particles connected by identical nonlinear springs. We prove the existence of micropteron traveling waves in the diatomic FPUT lattice in the limit as…
The delay Lotka-Volterra and delay Toda lattice equations are delay-differential extensions of the well-known soliton equations, the Lotka-Volterra and Toda lattice equations, respectively. This paper investigates integrable properties of…
The Kondo-lattice model describes a typical spin-charge coupled system in which localized spins and itinerant electrons are strongly coupled via exchange interactions and exhibits a variety of long-wavelength magnetic orders originating…
We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete…
Within the framework of the Inverse-Scattering formalism and the Hirota algorithm, soliton solutions of evolution equations are images of {\tau}-functions. Typically, the latter are expressed in terms of exponentials, the arguments of which…
The soliton resolution conjecture states that solutions to solitonic equations with generic initial data should, after some non--linear behaviour, eventually resolve into a finite number of solitons plus a radiative term. This conjecture is…
We consider a randomly perturbed Korteweg-de Vries equation. The perturbation is a random potential depending both on space and time, with a white noise behavior in time, and a regular, but stationary behavior in space. We investigate the…
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that…
The paper is focused on the dynamic homogenization of lattice-like materials with lumped mass at the nodes to obtain energetically consistent models providing accurate descriptions of the acoustic behavior of the discrete system. The…
The pioneering computer simulations of the energy relaxation mechanisms performed by Fermi, Pasta and Ulam can be considered as the first attempt of understanding energy relaxation and thus heat conduction in lattices of nonlinear…
Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a…
This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…
We analyze the origin and features of localized excitations in a discrete two-dimensional Hamiltonian lattice. The lattice obeys discrete translational symmetry, and the localized excitations exist because of the presence of nonlinearities.…
Characteristic features of soliton-comb structures in optical microresonators are investigated in normal and anomalous dispersion regimes, when the detuning parameter is varied over a broad range of values. The study rests on the assumption…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…
We study the mobility of solitons in second-harmonic-generating lattices. Contrary to what is known for their cubic counterparts, discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two…
The soliton resolution conjecture is one of the most interesting open problems in the theory of nonlinear dispersive equations. Roughly speaking it asserts that a solution with generic initial condition converges to a finite number of…
The lifetimes of localized nonlinear modes in both the $\beta$-Fermi-Pasta-Ulam-Tsingou ($\beta$-FPUT) chain and a cubic $\beta$-FPUT lattice are studied as functions of perturbation amplitude, and by extension, the relative strength of the…
We study the existence of traveling waves in a spring dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. This is a one-dimensional lattice of identical particles connected by alternating nonlinear springs. Following the work of Faver and Wright…