We explore the nonlinear gain coupled Schrödinger system through the utilization of the variables separation method and ansatz technique.By employing these approaches,we generate hierarchies of explicit dissipati...We explore the nonlinear gain coupled Schrödinger system through the utilization of the variables separation method and ansatz technique.By employing these approaches,we generate hierarchies of explicit dissipative vector vortices(DVVs)that possess diverse vorticity values.Numerous fundamental characteristics of the DVVs are examined,encompassing amplitude profiles,energy fluxes,parameter effects,as well as linear and dynamic stability.展开更多
The exact chirped soliton-like and quasi-periodic wave solutions of (2+1)-dimensional generalized nonlinearSchrodinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detail...The exact chirped soliton-like and quasi-periodic wave solutions of (2+1)-dimensional generalized nonlinearSchrodinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detailedly in thispaper.The form and the behavior of solutions are strongly affected by the modulation of both the dispersion coefhcientand the nonlinearity coefficient.In addition,self-similar soliton-like waves precisely piloted from our obtained solutionsby tailoring the dispersion and linear gain (loss).展开更多
Compression and stretching of ring-vortex solitons, which is a novel self-similar solution of(2+1)-dimensional diffraction decreasing waveguide, is investigated analytically and numerically. We obtain the ring-vortex ...Compression and stretching of ring-vortex solitons, which is a novel self-similar solution of(2+1)-dimensional diffraction decreasing waveguide, is investigated analytically and numerically. We obtain the ring-vortex solitons via the similarity transformation method. The distance modulation for the width, the diffraction, and the nonlinear response, strongly affects the form and the behavior of the self-similar vortex, and facilitates the efficient compression of optical waves. This approximate ring-vortex solitons can reflect the real properties of self-similar optical vortex beams during propagation under certain parameter window selection. Specific examples and figures are given to illustrate discussed features. The results obtained in this paper may have potential values for all-optical data-processing schemes and the design of beam compressors and amplifiers.展开更多
The Baecklund transformation and variable separation approach are developed for sine-Gordon systems. Three new types of variable separated solutions with some arbitrary functions have been obtained. A new kind of ghos...The Baecklund transformation and variable separation approach are developed for sine-Gordon systems. Three new types of variable separated solutions with some arbitrary functions have been obtained. A new kind of ghoston structure, which is invisible at most of time and can only be detected when it meets with a foldon, is found. This new structure shows a novel interesting and mysterious phenomenon.展开更多
The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstl...The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.展开更多
With the help of self-similarity transformation, we construct and study the nonautonomous vortices with different topological charges inside a planar graded-index nonlinear waveguide, analytically, and numerically. Al...With the help of self-similarity transformation, we construct and study the nonautonomous vortices with different topological charges inside a planar graded-index nonlinear waveguide, analytically, and numerically. Although these vortices are approximate, they can reflect the real properties of self-similar optical beam during a short-term propagation. Existence of these autonomous vortices require delicate balances between the system parameters such as diffraction, nonlinearity, gain, and external potential. We are concerned with some special but interesting situations, and discussing the changes of the height, width, energy, and central position of the vortices as the increase of propagation distance. Moreover, we are also interested in the azimuthal modulational instability of the system, and comparing our prediction for the modulational instability growth rates to numerical results.展开更多
In this paper, by solving a complex nonlinear Schr¨odinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonli...In this paper, by solving a complex nonlinear Schr¨odinger 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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11705164 and 11874324).
文摘We explore the nonlinear gain coupled Schrödinger system through the utilization of the variables separation method and ansatz technique.By employing these approaches,we generate hierarchies of explicit dissipative vector vortices(DVVs)that possess diverse vorticity values.Numerous fundamental characteristics of the DVVs are examined,encompassing amplitude profiles,energy fluxes,parameter effects,as well as linear and dynamic stability.
基金Supported by the National Natural Science Foundation of China under Grant No.11072219the Zhejiang Provincial Natural Science Foundation under Grant No.Y1100099
文摘The exact chirped soliton-like and quasi-periodic wave solutions of (2+1)-dimensional generalized nonlinearSchrodinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detailedly in thispaper.The form and the behavior of solutions are strongly affected by the modulation of both the dispersion coefhcientand the nonlinearity coefficient.In addition,self-similar soliton-like waves precisely piloted from our obtained solutionsby tailoring the dispersion and linear gain (loss).
文摘Compression and stretching of ring-vortex solitons, which is a novel self-similar solution of(2+1)-dimensional diffraction decreasing waveguide, is investigated analytically and numerically. We obtain the ring-vortex solitons via the similarity transformation method. The distance modulation for the width, the diffraction, and the nonlinear response, strongly affects the form and the behavior of the self-similar vortex, and facilitates the efficient compression of optical waves. This approximate ring-vortex solitons can reflect the real properties of self-similar optical vortex beams during propagation under certain parameter window selection. Specific examples and figures are given to illustrate discussed features. The results obtained in this paper may have potential values for all-optical data-processing schemes and the design of beam compressors and amplifiers.
文摘The Baecklund transformation and variable separation approach are developed for sine-Gordon systems. Three new types of variable separated solutions with some arbitrary functions have been obtained. A new kind of ghoston structure, which is invisible at most of time and can only be detected when it meets with a foldon, is found. This new structure shows a novel interesting and mysterious phenomenon.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11874324 and 11705164)the Natural Science Foundation of Zhejiang Province of China(Grant Nos.LY17A040011,LY17F050011,and LR20A050001)+1 种基金the Foundation of “New Century 151 Talent Engineering” of Zhejiang Province of Chinathe Youth Talent Program of Zhejiang A&F University
文摘The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.
文摘With the help of self-similarity transformation, we construct and study the nonautonomous vortices with different topological charges inside a planar graded-index nonlinear waveguide, analytically, and numerically. Although these vortices are approximate, they can reflect the real properties of self-similar optical beam during a short-term propagation. Existence of these autonomous vortices require delicate balances between the system parameters such as diffraction, nonlinearity, gain, and external potential. We are concerned with some special but interesting situations, and discussing the changes of the height, width, energy, and central position of the vortices as the increase of propagation distance. Moreover, we are also interested in the azimuthal modulational instability of the system, and comparing our prediction for the modulational instability growth rates to numerical results.
基金Supported by the National Natural Science Foundation of China under Grant No.11705164the Zhejiang Provincial Natural Science Foundation of China under Grant No.LQ16A040003
文摘In this paper, by solving a complex nonlinear Schr¨odinger 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.
