Search results for "solitary wave"
showing 10 items of 11 documents
Regular and singular pulse and front solutions and possible isochronous behavior in the Extended-Reduced Ostrovsky Equation: Phase-plane, multi-infin…
2016
In this paper we employ three recent analytical approaches to investigate several classes of traveling wave solutions of the so-called extended-reduced Ostrovsky Equation (exROE). A recent extension of phase-plane analysis is first employed to show the existence of breaking kink wave solutions and smooth periodic wave (compacton) solutions. Next, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of the traveling-wave equations for the exROE equation. These correspond to pulse solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddl…
Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and …
2014
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively o…
Granular chains for the assessment of thermal stress in slender structures
2015
Slender beams subjected to compressive stress are common in civil and mechanical engineering. The rapid in-situ measurement of this stress may prevent structural anomalies. In this paper, we describe the coupling mechanism between highly nonlinear solitary waves (HNSWs) propagating along an L-shaped granular system and a beam in contact with the granular medium. We evaluate the use of HNSWs as a tool to measure stress in thermally loaded structures and to estimate the neutral temperature, i.e. the temperature at which this stress is null. We investigated numerically and experimentally one and two L-shaped chains of spherical particles in contact with a prismatic beam subjected to heat. We f…
Convergent Analytic Solutions for Homoclinic Orbits in Reversible and Non-reversible Systems
2013
In this paper, convergent, multi-infinite, series solutions are derived for the homoclinic orbits of a canonical fourth-order ODE system, in both reversible and non-reversible cases. This ODE includes traveling-wave reductions of many important nonlinear PDEs or PDE systems, for which these analytical solutions would correspond to regular or localized pulses of the PDE. As such, the homoclinic solutions derived here are clearly topical, and they are shown to match closely to earlier results obtained by homoclinic numerical shooting. In addition, the results for the non-reversible case go beyond those that have been typically considered in analyses conducted within bifurcation-theoretic sett…
GROUP ANALYSIS AND SOME EXACT SOLUTIONS FOR THE THERMAL BOUNDARY LAYER
2006
We perform the group analysis of the thermal boundary layer in laminar flow. We obtain the classification of the solutions in terms of the asymptotic velocity. Some solutions of the boundary layer equations, for some distributions of outer flow velocity, are obtained also.
On the coupling dynamics between thermally stressed beams and granular chains
2015
The in-situ measurement of thermal stress in slender beams, or long continuous welded rails, may prevent structural anomalies. With this aim, we investigated the coupling dynamics between a beam and the highly nonlinear solitary waves propagating along a straight granular chain in contact with the beam. We hypothesized that these waves can be used to measure the stress of thermally loaded structures, or to infer the neutral temperature, i.e., the temperature at which this stress is null. We studied numerically and experimentally the mechanical interaction of one and two straight chains of spherical particles in contact with a prismatic beam that is subjected to heat. The results show that c…
On the Use of L-shaped Granular Chains for the Assessment of Thermal Stress in Slender Structures
2014
Slender beams subjected to compressive load are common in civil engineering. The rapid in-situ measurement of this stress may help preventing structural anomalies. In this article, we describe the coupling mechanism between highly nonlinear solitary waves (HNSWs) propagating along an L- shaped granular system and a beam in contact with the gran- ular medium. We evaluate the use of these waves to measure stress in thermally loaded structures and to estimate the neutral temperature, i.e. the temperature at which the stress is null. We investigate numerically and experimentally one and two L- shaped chains of spherical particles in contact with a prismatic beam subjected to heat. We find that …
A microscopic monomeric mechanism for interpreting intrinsic optical bistability observed in Yb3+-doped bromide materials
2004
We present a mechanism able to show intrinsic bistable behaviour involving single Yb3+ ions embedded into bromide lattices, in which intrinsic optical bistability (IOB) has been observed. The mechanism is based on the experimentally found coupling between the Yb3+ ion and the totally symmetric local mode of vibration of the [YbBr6]3- coordination unit. The model reproduces the IOB observed in CsCdBr3:1% Yb3+ and allows to understand the experimentally found presence of the phenomenon in the other bromides, but its absence in Cs3Lu2Cl9:Yb3+.
Transverse instability of periodic and generalized solitary waves for a fifth-order KP model
2017
We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.
Corrigendum to “Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infi…
2022
Section 7 of the original paper contained several errors which are corrected here. Equations (54) and (55) are incorrect. In the following, the corrected versions of these equations are given and the subsequent results of Section 7 are also revised.