Transition,coexistence, and interaction of vector localized waves arising from higher-order effects

We study vector localized waves on continuous wave background with higher-order effects in a two-mode optical fiber. The striking properties of transition, coexistence, and interaction of these localized waves arising from higher-order effects are revealed in combination with corresponding modulation instability (MI) characteristics. It shows that these vector localized wave properties have no analogues in the case without higher-order effects. Specifically, compared to the scalar case, an intriguing transition between bright–dark rogue waves and w-shaped–anti-w-shaped solitons, which occurs as a result of the attenuation of MI growth rate to vanishing in the zero-frequency perturbation region, is exhibited with the relative background frequency. In particular, our results show that the w-shaped–anti-w-shaped solitons can coexist with breathers, coinciding with the MI analysis where the coexistence condition is a mixture of a modulation stability and MI region. It is interesting that their interaction is inelastic and describes a fusion process. In addition, we demonstrate an annihilation phenomenon for the interaction of two w-shaped solitons which is identified essentially as an inelastic collision in this system.     

Resolvent Estimates for Boundary Value Problems on Large Intervals Via the Theory of Discrete Approximations

In many applications such as the stability analysis of traveling waves, it is important to know the spectral properties of a linear differential operator on the whole real line. We investigate the approximation of this operator and its spectrum by finite interval boundary value problems from an abstract point of view. Under suitable assumptions on the boundary operators, we prove that the approximations converge regularly (in the sense of discrete approximations) to the all line problem, which has strong implications for the behavior of resolvents and spectra. As an application, we obtain resolvent estimates for abstract coupled hyperbolic–parabolic equations. Furthermore, we show that our results apply to the FitzHugh–Nagumo system.     

Travelling waves associated with saddle-node bifurcation in weakly coupled CML

Weakly coupled CML can be analytically solved by using perturbative methods. This technique has been recently used to deduce analytical expressions for travelling waves. Nonetheless, the results were limited for periodic solutions far away from saddle-node bifurcation. In this Letter, this problem is solved and periodic solutions, arising from the individual dynamics, are totally characterised.     

Fundamental theories of waves and particles formulated without classical mass

Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called ‘wave mass’, which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.     

Hardy type inequality and application to the stability of degenerate stationary waves

This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous conservation laws in the half space. It is proved that the solution converges to the corresponding degenerate stationary wave at the rate t−α/4 as t→∞, provided that the initial perturbation is in the weighted space for α<αc(q):=3+2/q, where q is the degeneracy exponent. This restriction on α is best possible in the sense that the corresponding linearized operator cannot be dissipative in for α>αc(q). Our stability analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant.     

Exact travelling wave solutions of the generalized Bretherton equation

We search for exact travelling wave solutions of the generalized Bretherton equation for integer, greater than one, values of the exponent m of the nonlinear term by two methods: the truncated Painlevé expansion method and an algebraic method. We find periodic solutions for m=2 and m=5, to add to those already known for m=3; in all three cases these solutions exist for finite intervals of the wave velocity. We also find a “kink” shaped solitary wave for m=5 and a family of elementary unbounded solutions for arbitrary m.     

浅水长波近似方程组的拟小波解

以浅水长波近似方程组为例,提出了拟小波方法求解(1 1)维非线性偏微分方程组数值解,该方程用拟小波离散格式离散空间导数,得到关于时间的常微分方程组,用四阶Runge-K utta方法离散时间导数,并将其拟小波解与解析解进行比较和验证.     

Asymptotic and numerical analysis of thermoelastic waves in an isotropic plate

^** Email: n.scott{at}uea.ac.uk This paper considers the propagation of a plane thermoelasticwave in an infinite homogeneous isotropic plate subjected toeither isothermal or thermally insulated traction-free boundaryconditions. The primary concerns are the derivation and numericalexamination of the dispersion relations along with the developmentof asymptotic models for the fundamental branches of the dispersionrelations. Thermal dissipation is also discussed.     

High frequency SAW devices based on third harmonic generation

We demonstrate the third harmonic generation in a ZnO/Si layered structure to obtain high frequency SAW devices. This configuration eliminates the need of high lithography resolution and allows easy integration of such devices and electronics on the same wafer. A theoretical study was carried out for the determination of the phase velocity and the electromechanical coupling coefficient (K²) dispersion curves of the surface acoustic waves. These results are also in agreement with those measured on a SAW filter designed for the third harmonic generation and the operating frequency is up to 2468 MHz.