相关论文: Coherent structures in long range FPUT lattices, P…
We study the propagation of solitary waves in a Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with small random heterogeneity in the linear spring force. Perturbed by the random environment, solitary waves lose energy through a radiative tail,…
We study the interaction of small amplitude, long wavelength solitary waves in the Fermi-Pasta-Ulam model with general nearest-neighbor interaction potential. We establish global-in-time existence and stability of counter-propagating…
We prove the existence of solitary waves in a lattice where all particles interact with each other by pair-wise repulsive forces that decay with distance. The variational existence proof is based on constrained optimization and provides a…
This paper concerns the existence of generalized solitary waves (solitary waves with small ripples at infinity) for a diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. It is proved that the FPUT lattice problem has a generalized…
In this paper, we study the smooth transition from solitons to solitary waves in localization, relation between energy and velocity, propagation and scattering property in the Fermi-Pasta-Ulam lattice analytically and numerically. A soliton…
We give a rigorous proof of existence for solitary waves of a peridynamics model in one space dimension recently investigated by Silling (J. Mech. Phys. Solids 96:121--132, 2016). We adapt the variational framework developed by Friesecke…
We consider a class of fully-nonlinear Fermi-Pasta-Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order $\alpha >1$. This class of systems incorporates a classical Hertzian model…
We study the existence of solitary waves in a diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. For monatomic FPUT the traveling wave equations are a regular perturbation of the Korteweg-de Vries (KdV) equation's but, surprisingly, we find…
In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $\alpha$-Fermi-Pasta-Ulam type with the additional feature…
We use a specialized boundary-value problem solver for mixed-type functional differential equations to numerically examine the landscape of traveling wave solutions to the diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) problem. By using a…
We study the existence of solitary-wave solutions and some of their properties for a general multicomponent long-wave-short-wave interaction system. The system considered here describes the nonlinear interaction of multiple short waves with…
In this paper we consider a three-component system of one dimensional long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We prove orbital stability of the solitary wave solutions…
We prove the existence of small-amplitude periodic traveling waves in dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattices without assumptions of physical symmetry. Such lattices are infinite, one-dimensional chains of coupled particles in which…
We consider a Fermi-Pasta-Ulam-Tsingou lattice with randomly varying coefficients. We discover a relatively simple condition which when placed on the nature of the randomness allows us to prove that small amplitude/long wavelength solutions…
We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $\alpha+1$ with $\frac43<\alpha<3$, we employ…
The generalized Levy-Leblond equation for a $(3+1)$-dimensional self-interacting Fermi field is considered. Spin up solitary wave solutions with space oscillations in the $x^3$-coordinate are constructed. The solutions are shown to…
The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate…
A family of solitary waves is constructed in Frenkel-Kontorova model and its continuum and quasi-continuum approximations. Each solitary waves is characterised by the number of local maxima in its profile and a relation between external…
Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…
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…