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We report the first gain-managed nonlinear amplifier operating in burst mode, delivering 50-fs, 600- nJ pulses. Due to a complex interplay between nonlinearity and gain, the amplification is influenced non- trivially and collectively by all the pulses within a burst.

We show the existence of two nontrivial nonnegative solutions and infinitely many solutions for degeneratep(x)-Laplace equations involving concave-convex type nonlinearities with two parameters. By investigating the order of concave and convex terms and using a variational method, we determine the existence according to the range of each parameter. Some Caffarelli-Kohn-Nirenberg type problems with variable exponents are also discussed. 2010Mathematics Subject Classification: 35J20, 35J60, 35J70, 47J10, 46E35. Key words and phrases:p(x)-Laplacian,Weighted variable exponent Lebesgue-Sobolev spaces, Concave-convex nonlinearities, Nonnegative solutions, Multiplicity.

Retaining an imprint of their thermal history is a hallmark of glassy materials. Although its microscopic origin is still in debate, this memory effect is the potential to be utilized in engineering applications as a way to rejuvenate the glasses. For a better understanding of it, we investigated how the memory effect is affected by non-exponentiality and non-linearity, which are two basic features of glass dynamics. A mathematical model with a linear superposition of relaxation functions at a series of experienced temperatures was employed to reproduce the memory effect. The results demonstrate that non-exponentiality has a leading role in determining memory behaviors while non-linearity influences it weakly. An enhanced memory effect found in a recent multistep temperature training experiment is understood with the decreasing non-exponentiality caused by the increasing dynamical heterogeneities of the system. This work provides a guide to regulating the memory effect in practical applications.

The article focuses on a fractional Choquard equation with critical nonlinearities. By means of variational methods, the article verifies that nontrivial solutions to the equation exist.

The emerging interest in integrated optical technologies raises the need for precise characterisation techniques for waveguides presenting nonlinearities. Here we propose a non-interferometric measurement to accurately characterise the Kerr contribution in hybrid waveguides and illustrate its performances using SiN waveguides with a GSS chalcogenide top-layer. The sensitivity of our technique in terms of nonlinear phase reaches 10 mrad and its accuracy makes possible to extract the nonlinear contributions from the top-layer.

A (2+1)-dimensional N -coupled nonlinear Schrödinger equation with spatially modulated cubic–quintic nonlinearity and transverse modulation is studied, and vector multipole and vortex soliton solutions are analytically obtained. When the modulation depth q is chosen as 0 and 1, vector multipole and vortex solitons are constructed, respectively. The number of “petals” for the multipole solitons and vortex solitons is related to the value of the topological charge m , and the number of layers in the multipole solitons and vortex solitons is determined by the value of the soliton order number n .

Harmonic generation measurement is recognized as a promising tool for inspecting material state or micro-damage and is an ongoing research topic. Second harmonic generation is most frequently employed and provides the quadratic nonlinearity parameter (β) that is calculated by the measurement of fundamental and second harmonic amplitudes. The cubic nonlinearity parameter (β2), which dominates the third harmonic amplitude and is obtained by third harmonic generation, is often used as a more sensitive parameter in many applications. This paper presents a detailed procedure for determining the correct β2 of ductile polycrystalline metal samples such as aluminum alloys when there exists source nonlinearity. The procedure includes receiver calibration, diffraction, and attenuation correction and, more importantly, source nonlinearity correction for third harmonic amplitudes. The effect of these corrections on the measurement of β2 is presented for aluminum specimens of various thicknesses at various input power levels. By correcting the source nonlinearity of the third harmonic and further verifying the approximate relationship between the cubic nonlinearity parameter and the square of the quadratic nonlinearity parameter (β∗β), β2≈β∗β, the cubic nonlinearity parameters could be accurately determined even with thinner samples and lower input voltages.

In this paper, on the one hand, we prove that for n≥2 any subbundle of T∗Tn with bounded fibers symplectically embeds into a trivial subbundle of T∗Tn where the fiber is an irrational cylinder. This not only resolves an open problem in Gong and Xue (Nonlinearity 33:6297–6348, 2020) (which was stated for the 4-dimension case, that is, n=2) and also generalizes to any higher-dimensional situation. The proof is based on some version of Dirichlet’s approximation theorem. On the other hand, we generalize a main result in Gong and Xue (Nonlinearity 33:6297–6348, 2020), showing that any π~1(M)-trivial Liouville diffeomorphism on T∗M (for instance, a diffeomorphism induced by an isometry on M) does not change the full marked length spectrum of a Finsler metric F on M, up to a lifting of the Finsler metric F to the unit codisk bundle DF∗M. The proof is based on persistence module theory.

The resonant behavior of one-way Lamb and SH (shear horizontal) mixing method in composite laminates with transverse-isotropic quadratic nonlinearity is investigated through numerical simulations in this paper. Different from previous studies, the composite constitutive model is combined from orthotropic elasticity and transverse-isotropic quadratic nonlinearity, which is implemented by ABAQUS/VUMAT subroutine. When two fundamental waves ( S 0 -mode Lamb waves and SH 0 waves) mix in composite laminates with quadratic nonlinearity, the resonant SH 0 waves can be generated with the resonance condition ω S 0 / ω SH 0 = 2 κ /( κ + 1). Meanwhile, the relationships between the acoustic nonlinear parameter (ANP) and damage degree, fundamental frequency, frequency deviation, propagation distance are also investigated. Moreover, the method of locating the damage region in composite laminates is proposed and verified by using the resonant wave time-domain signal.

This study addresses the adaptive tracking control problem for a class of time-delay systems in strict-feedback form with unknown control gains and uncertain actuator non-linearity. The actuator non-linearity can be either backlash or dead zone, and the proposed approach does not require the knowledge of the bounds of non-linearity parameters. By applying an appropriate Lyapunov–Krasovskii functional and utilising the property of the well-defined trigonometric functions, the problems of time delay and controller singularity are avoided. The feasibility of using a static neural network to attenuate the effect of actuator non-linearity is proved with the aid of intermediate value theorem. Furthermore, it is proved that all closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Two simulation examples are provided to demonstrate the effectiveness of the designed method.