Search results for "equation"
showing 10 items of 4219 documents
Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations
2014
In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations. A recent, novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of three of the GCH NLPDEs, i.e. the possible non-smooth peakon, cuspon and compacton solutions. Two of the GCH equations do not support singular traveling waves. The third equation supports four-segmented, non-smooth $M$-wave solutions, while the fourth supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes. Moreover, sm…
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…
Stability of the equilibrium state of the equation system of a viscous barotropic gas in the model of atmosphere
2006
We consider the system of equations of viscous gas motion whose pressure is related to the density by the law $p = h \varrho^\gamma$ with 1<γ <2, in a domain defined by two levels of geopotential. Under the force due to geopotential and the Coriolis force, we prove the stability of the equilibrium state in a suitable Sobolev space. Keywords: Viscous barotropic gas, Equilibrium state, Coriolis force Mathematics Subject Classification (2000): 35Q35, 76N15
First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities
2022
[EN] Random initial value problems to non-homogeneous first-order linear differential equations with complex coefficients are probabilistically solved by computing the first probability density of the solution. For the sake of generality, coefficients and initial condition are assumed to be absolutely continuous complex random variables with an arbitrary joint probability density function. The probability of stability, as well as the density of the equilibrium point, are explicitly determined. The Random Variable Transformation technique is extensively utilized to conduct the overall analysis. Several examples are included to illustrate all the theoretical findings.
Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization
2003
This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of…
Singularity tracking for Camassa-Holm and Prandtl's equations
2006
In this paper we consider the phenomenon of singularity formation for the Camassa-Holm equation and for Prandtl's equations. We solve these equations using spectral methods. Then we track the singularity in the complex plane estimating the rate of decay of the Fourier spectrum. This method allows us to follow the process of the singularity formation as the singularity approaches the real axis.
Heterogeneous Firms, Globalisation and the Distance Puzzle
2015
Despite the strong pace of globalisation, the distance effect on trade is persistent or even growing over time (Disdier and Head, 2008). To solve this distance puzzle, we use the recently developed gravity equation estimator from Helpman et al. (2008) (HMR henceforth). Using three different data sets, we find that the distance coefficient increases over time when ordinary least squares (OLS) is used, while the non-linear estimation of HMR leads to a decline in the distance coefficient over time. The distance puzzle, thus, arises from a growing bias of OLS estimates. The latter is explained by an increase in the importance of the bias from omitting the number of heterogeneous exporting firms…
Do nonreciprocal preferential trade agreements increase beneficiaries' exports?
2014
Abstract This paper investigates whether and to what extent nonreciprocal preferential trade agreements (NRPTAs) have increased developing countries' exports to richer countries. Using recent developments in the econometric analysis of the gravity equation over the period 1960–2008, we find robust evidence that, on the whole, NRPTAs and the Generalized System of Preferences have had an economically significant effect on exports from developing countries. However, the estimation of catch-all dummies masks heterogeneous results for the individual programs.
The impact of embassies and consulates on tourism
2007
Abstract This paper estimates the effect of embassies and consulates on tourist flows from the G-7 countries. The results indicate that embassies and consulates have a positive and significant effect on tourism that ranges between 15% and 30% depending on the estimation technique. Moreover, the impact is larger for the sample of developing countries. The disaggregated analysis shows that, after controlling for both origin and destination fixed effects, a significant impact is found in the seven origin countries.
A study on spectral optimisation in partial response CPM signals
1995
An optimisation technique for the minimisation of the effective bandwidth in partial response CPM signals is described. The minimum Euclidean distance is used as optimisation constraint because the bit error probability is a function of this parameter for high values of signal to noise ratio. The procedure has been implemented for a correlation length corresponding to two signalling intervals. The optimisation problem leads to a system of two nonlinear differential equations for the pulse shape, together with some boundary conditions. Numerical solution of the differential equations has been performed; initial conditions have been adjusted, to satisfy the boundary conditions using an iterat…