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The exact chirped soliton-like and quasi-periodic wave solutions of (2+1)-dimensional generalized nonlinear Schrödinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detailedly in this paper. The form and the behavior of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain (loss).

In this paper, the decomposition method is implemented for solving the bidirectional Sawada- Kotera (bSK) equation with two kinds of initial conditions. As a result, the Adomian polynomials have been calculated and the approximate and exact solutions of the bSK equation are obtained by means of Maple, such as solitary wave solutions, doubly-periodic solutions, two-soliton solutions. Moreover, we compare the approximate solution with the exact solution in a table and analyze the absolute error and the relative error. The results reported in this article provide further evidence of the usefulness of the Adomian decomposition method for obtaining solutions of nonlinear problems

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Ti3C2 nanosheet is a newly discovered two-dimensional (2D) clan. It turns out to have encouraging applications for electromagnetic shielding and energy storage. Here, Ag@ Ti3C2 hybrids are precisely synthesized by using the one-step solution processing method. Also, their ultrafast broadband nonlinear optical responses in the visible region are studied systematically through nanosecond open-aperture Z-scan and transient absorption techniques. The mechanism of two-photon absorption (TPA) is disclosed in the visible region (409–532 nm). When the laser energy is low and the wavelength is longer than 400 nm, nonlinear absorption cannot happen. Meanwhile, as the laser energy increases, two photons will be absorbed by the electrons in the valence band and the electrons will jump to the conduction band. The process is named as two-photon absorption which will make the specimen show reverse saturable absorption (RSA) properties. What is more, the ultrafast carrier dynamics of the specimen are studied by using the transient absorption. The result shows that the decay contains two phases: the fast and then the slow one. The two phases first come from electron–phonon and then from phonon–phonon interactions, respectively. The electron transfer and charge carrier trapping processes are further verified by the outcomes of similar measurements on Ag@ Ti3C2 hybrids. Besides, the two decay processes increase together with the pump fluence. These results show that Ti3C2 nanosheet has potential applications in broadband optical limiter.

Compression and stretching of ring-vortex solitons in a bulk nonlinear mediumLai Xian-Jing(来娴静) a)b) † , Cai Xiao-Ou(蔡晓鸥) b) , and Zhang Jie-Fang(张解放) a)c)

In this paper, by solving a complex nonlinear Schrödinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonlinear absorption gives rise to the stability of dissipative vortex solitons in self-defocusing nonlinear medium in the presence of constant linear gain. Numerical simulation reveals the interaction effect among linear gain and nonlinear loss in the azimuthal modulation instabilities of these vortices suppression. Apart from the uniform linear gain indeed affects the stability of vortex in this media, another noticeable feature of current setup is that the steep spatial modulation of the nonlinear absorption can suppress sidelobes effectively and support stable vortex solitons in situations with uniform linear gain. Under appropriate conditions, the vortex solitons can propagate stably and feature no symmetry breaking, although the beams exhibit radical compression and amplification as they propagate.