On the hysteresis phenomenon in the directly excited nonlinear resonant sloshing waves in a tank

Summary Steady nonlinear resonant standing waves obtained in a rectangular tank by a direct excitation are studied in detail both experimentally and numerically. The experimental study demonstrates the existence of a well defined hysteresis between two quite different wave distributions in the tank. The dissipation coefficient at the wavemaker is estimated from the present experimental results. Numerical simulations based on the solution of the nonlinear Schrödinger equation, with the dissipation coefficient at the wavemaker obtained experimentally, show that this hysteresis may be reproduced in calculations when a nonlinear boundary condition at the wavemaker is adopted. Such a boundary condition is indeed supported by experimental evidence.     

光纤中光孤子传输演化及相互作用研究

基于非线性薛定谔方程,采用分步傅立叶方法模拟了基阶、二阶和三阶皮秒光孤子以及光孤子对在光纤中的传输演化.结果表明,在长距离传输过程中基阶孤子的幅度和脉宽基本不变,是进行光孤子通信的理想载体.高阶孤子的幅度和脉宽变化较大,并呈现一种周期性的变化;孤子对的传输与两个脉冲的初始相位和输入强度相关.考虑三阶色散的飞秒量级孤子在光纤中的传输将不再出现对称性和周期性,脉冲的中心位置将发生偏移,同时脉冲的波形也会发生扭曲.     

Optical solitons in nonlinear directional couplers with spatio-temporal dispersion

This paper addresses solitons in nonlinear directional couplers in non-Kerr law media, with spatio-temporal dispersion. Both twin-core couplers as well as multiple-core couplers are studied. The nonlinearities studied are Kerr law, power law, parabolic law, dual-power law and log law. Bright, dark and singular soliton solutions of the governing equation are studied.     

High-order dark solitons in nonlocal nonlinear media

Abstract

The high-order dark solitons in nonlocal nonlinear media are found up to fifth-order. The stability of high-order dark solitons is investigated numerically. The stability relation graphs of negative imaginary eigenvalues versus propagation constant are obtained. The propagation graphs of the input signal with noise added prove the result of the stability analysis to be correct.     

Solitary stress waves in a nonlinear thermoelastic medium

The propagation process of solitary stress waves in a medium with five thermoelastic characteristics is investigated within the one-dimensional statement. Existence conditions and geometric characteristics of solitary waves are obtained, and restrictions are found for the elastic and thermal constants.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 61, No. 3, pp. 493–498, September, 1991.     

Spiralling elliptic vortex solitons in nonlocal nonlinear media

We have introduced a class of spiralling elliptic vortex (SEV) solitons in nonlocal nonlinear media. The SEV soliton has more complicated structures both in its amplitude and in its phase compared with conventional vortex solitons. Different from the circularly symmetric amplitude profile of vortex solitons, the SEV solitons exhibit the elliptic optical spots. Furthermore, the SEV solitons have the special modulated helical phase structures, which make the SEV solitons rotate. For different topological charges, all the SEV solitons own the same critical power, critical cross-term phase coefficient and the critical angular velocity for fixed semiaxis of the elliptic spots. The stability of the SEV solitons is confirmed by the direct numerical simulations with random noises.     

Existence of solitary waves in a nonlinear thermoelastic medium with prior deformations

In a geometrically one-dimensional nonlinear formulation, the existence of solitary waves of deformations in nonlinear thermoelastic previously stressed medium is studied. The speed of propagation of the waves is shown to depend on the initial deformations.Translated from Inzhernerno-fizicheskii Zhurnal, Vol. 61, No. 4, pp. 685–689, October, 1991.     

Single-mode operation in few-mode optical fibre based on resonant coupling

The design of a low-bending loss few-mode optical fibre is proposed. Low-bending loss for the fundamental mode is achieved by increasing the index contrast between the core and the cladding, and a microstructured mode filtering region is applied to filter out the higher-order modes in the fibre. Numerical results show that the fundamental mode loss is lower than 0.03 dB/turn and the high-order mode is higher than 4.4 dB/turn at the bending radius of 5 mm and 1300–1600 nm wavelength range.     

Weakly nonlinear stationary waves in a thin fluid film

Stationary periodic wave flow regimes of thin films of a viscous fluid on an inclined plane are considered.     

Soliton-like waves in a low temperature nonlinear thermoelastic solid

An analysis of soliton-like waves propagating in a low-temperature nonlinear thermoelastic solid given in J. Ignaczak, J. Thermal Stresses 13, 73–98 (1990) is extended by introducing a low-temperature parameter ω ? (0, 1 ] into the basic equations. The two ω-parametrized one-dimensional soliton-like thermoelastic waves that propagate with finite speeds in a given direction are obtained in an implicit form for a large range of other parameters involved, by using the method similar to that employed by Ignaczak. If ω = 1 the thermoelastic soliton-like waves from Ignaczak's article are recovered. In addition, on the basis of an approximate system of nonlinear governing equations valid for a small ω, two fast-moving soliton-like thermoelastic waves are examined in detail. Each of these two waves reveals a fountain effect in a neighborhood of a moving front, and is close to a thermodynamical equilibrium far from the front. Schematic graphs illustrate both the exact and the approximate soliton-like waves.     

水槽中的带隙孤子及其非线性响应

1引言近20年来,带隙孤子受到了研究人员的广泛关注。和禁带结构相伴,带隙孤子出现在Bragg光栅光纤,二维和三维光子晶体等许多光学结构中。与一般的包络孤子不同,带隙孤子的谱带位于线性波禁     

Envelope shock waves in nonlinear systems with mode coupling

It is shown that the dispersion of nonlinearity in waveguide structures admitting strong linear coupling between two unidirectional waves significantly affects the dynamics of the wave packet propagation. In a nonamplifying medium, there is a principal possibility (not inherent in one-wave structures) that an envelope shock wave would form on the leading front of the wave packet.     

Rogue waves generation in a left-handed nonlinear transmission line with series varactor diodes

We investigate the electromagnetic wave behavior and its characterization using collective variables technique. Second-order dispersion, first- and second-order nonlinearities, which strongly act in a left-handed nonlinear transmission line with series varactor diodes, are taken into account. Four frequency ranges have been found. The first one gives the so-called energetic soliton due to a perfect combination of second-order dispersion and first-order nonlinearity. The second frequency range presents a dispersive soliton leading to the collapse of the electromagnetic wave at the third frequency range. But the fourth one shows physical conditions which are able to provoke the appearance of wave trains generation with some particular waves, the rogue waves. Moreover, we demonstrate that the number of rogue waves increases with frequency. The soliton, thereafter, gains a relative stability when second-order nonlinearity comes into play with some specific values in the fourth frequency range. Furthermore, the stability conditions of the electromagnetic wave at high frequencies have been also discussed.     

Existence of solitary waves in a prestressed nonlinear thermoelastic medium with dry friction

V. I. Lenin Belorussian State University, Minsk. Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 62, No. 1, pp. 140–145, January, 1992.     

Periodic soliton trains in nonlinear magneto-optical media

The combination of the vector nature (i.e. polarization) of light in materials with nonlinearity can give rise to outstanding phenomena in the transmission of nonlinear optical fields. When the optical medium has been initially altered by a magnetic field, magneto-optical effects introduce additional interesting phenomena such as the possible control of optical signals by a magnetic field. The present work addresses the problem of optical-soliton generation from pulsed radiations interacting with a quasi-resonant magneto-optical medium, under normal Zeeman effect. It is shown that multi-soliton structures can be generated in the magneto-optical medium under specific conditions, these include periodic trains of bright and dark optical solitons having finite temporal periods.     

Evolution equations for nonlinear waves in a tapered elastic tube filled with a viscous fluid

In this work, employing the reductive perturbation method and treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube, the propagation of weakly nonlinear waves is investigated in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, depending on the viscosity and perturbation parameters we obtained various evolution equations as the extended Korteweg-de Vries (KdV), extended KdV Burgers and extended perturbed KdV equations. Progressive wave solutions to these evolution equations are obtained and it is observed that the wave speeds increase with the distance for negative tapering while they decrease for positive tapering.     

Optical solitons of some fractional differential equations in nonlinear optics

This paper deals with two different forms of the conformable fractional Benjamin–Bona–Mahony (BBM) equations by an analytical method. These physical models have important applications for describing the propagation of optical pulses in non-linear media. The conformable fractional symmetric BBM equation and the conformable time fractional Equal-width (EW) equation are considered. The extended Jacobi’s elliptic function expansion scheme are used to extract explicit solitons.