We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms.By means of the modified squared wavefunction method,we obtain...We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms.By means of the modified squared wavefunction method,we obtain the Jacobi's elliptic solution of the defocusing Hirota equation,and solve the related linear matrix eigenvalue problem on elliptic function background.The elliptic N-dark soliton solution in terms of theta functions is constructed by the Darboux transformation and limit technique.The asymptotic dynamical behaviors for the elliptic N-dark soliton solution as t→±∞are studied.Through numerical plots of the elliptic one-,two-and three-dark solitons,the amplification effect on the velocity of elliptic dark solitons,and the compression effect on the soliton spatiotemporal distributions produced by the third-order dispersion and self-steepening terms are discussed.展开更多
In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,where...In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.展开更多
In order to more accurately and effectively consider the propagation process of solitons in electromagnetic pulse waves and make full use of wavelength division multiplexing,we study a class of high-order three-compon...In order to more accurately and effectively consider the propagation process of solitons in electromagnetic pulse waves and make full use of wavelength division multiplexing,we study a class of high-order three-component Hirota equations by the Riemann-Hilbert method.Under zero boundary conditions and given initial conditions q_(j)(x,0),the N-soliton solutions of the equations are obtained by constructing and solving Riemann-Hilbert problems based on matrix spectral problem.Specifically,we discuss the cases of N=1,2,analyze the dynamical properties of 1-soliton and 2-soliton solutions through numerical simulations,and summarize the effect of integrable perturbations and spectral parameters on soliton motion.展开更多
Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pol...Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12326304,12326305,12071304)the Shenzhen Natural Science Fund(the Stable Support Plan Program)(Grant No.20220809163103001)+2 种基金the Natural Science Foundation of Henan Province(Grant No.232300420119)the Excellent Science and Technology Innovation Talent Support Program of ZUT(Grant No.K2023YXRC06)Funding for the Enhancement Program of Advantageous Discipline Strength of ZUT(2022)。
文摘We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms.By means of the modified squared wavefunction method,we obtain the Jacobi's elliptic solution of the defocusing Hirota equation,and solve the related linear matrix eigenvalue problem on elliptic function background.The elliptic N-dark soliton solution in terms of theta functions is constructed by the Darboux transformation and limit technique.The asymptotic dynamical behaviors for the elliptic N-dark soliton solution as t→±∞are studied.Through numerical plots of the elliptic one-,two-and three-dark solitons,the amplification effect on the velocity of elliptic dark solitons,and the compression effect on the soliton spatiotemporal distributions produced by the third-order dispersion and self-steepening terms are discussed.
基金supported by the National Natural Science Foundation of China under Grant No.12147115the Discipline(Subject)Leader Cultivation Project of Universities in Anhui Province under Grant Nos.DTR2023052 and DTR2024046+2 种基金the Natural Science Research Project of Universities in Anhui Province under Grant No.2024AH040202the Young Top Notch Talents and Young Scholars of High End Talent Introduction and Cultivation Action Project in Anhui Provincethe Scientific Research Foundation Funded Project of Chuzhou University under Grant Nos.2022qd022 and 2022qd038。
文摘In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.
基金Project supported by Shaanxi Scholarship Council of China(Grant No.2021-030)the Youth Scientific Research Project of Shaanxi Province,China(Grant No.202103021223060)。
文摘In order to more accurately and effectively consider the propagation process of solitons in electromagnetic pulse waves and make full use of wavelength division multiplexing,we study a class of high-order three-component Hirota equations by the Riemann-Hilbert method.Under zero boundary conditions and given initial conditions q_(j)(x,0),the N-soliton solutions of the equations are obtained by constructing and solving Riemann-Hilbert problems based on matrix spectral problem.Specifically,we discuss the cases of N=1,2,analyze the dynamical properties of 1-soliton and 2-soliton solutions through numerical simulations,and summarize the effect of integrable perturbations and spectral parameters on soliton motion.
基金Supported by the National Natural Science Foundation of China (12074295)。
文摘Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.
