相关论文: The Short Pulse Hierarchy

In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special Hamiltonians are given in terms of elliptic…

We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic…

We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges following from the Lax equation, much like…

Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…

Propagation of the extremely short electromagnetic pulse in non-linear dielectric media without the slowly varying envelope approximation is discussed. The models under consideration take into account both resonant and not-resonant…

The distinctive features of passing the two-component extremely short pulses through the nonlinear media are discussed. The equations considered describe the propagation in the two-level anisotropic medium of the electromagnetic pulses…

Integrable self-adaptive moving mesh schemes for short pulse type equations (the short pulse equation, the coupled short pulse equation, and the complex short pulse equation) are investigated. Two systematic methods, one is based on…

This work is focused on a nonlinear equation describing the oscillations of an extensible viscoelastic beam with fixed ends, subject to distributed elastic external force. For a general axial load $\beta$, the existence of a finite/infinite…

Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…

Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the…

In the present paper, we propose a complex short pulse equation and a coupled complex short equation to describe ultra-short pulse propagation in optical fibers. They are shown to be integrable due to the existence of Lax pairs and infinite…

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling…

We obtain the bi-Hamiltonian structure for some of the two-component short pulse equations proposed in the literature to generalize the original short pulse equation when polarized pulses propagate in anisotropic media.

We study the short pulse dynamics in the deterministic and stochastic environment in this thesis. The integrable short pulse equation is a modelling equation for ultra-short pulse propagation in the infrared range in the optical fibers. We…

Nonlinear evolutions of an ultra-intense, short laser pulse due to the wake excitation inside the plasma are studied by means of detailed Particle-In-Cell (PIC) simulations and comprehensive analyses. Pulse lengths both longer and shorter…

We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…

We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations…

We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. In the frequency "band gaps" (where linear electromagnetic waves are evanescent) with linear…

The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global…

We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium…