N-kink soliton and high-order synchronized breather solutions for potential Kadomtsev-Petviashvili equation are derived by means of the Hirota bilinear method,and the limit process of high-order synchronized breathers...N-kink soliton and high-order synchronized breather solutions for potential Kadomtsev-Petviashvili equation are derived by means of the Hirota bilinear method,and the limit process of high-order synchronized breathers are shown.Furthermore,M-lump solutions are also presented by taking the long wave limit.Additionally,a family of semi-rational solutions with elastic collision are generated by taking a long-wave limit of only a part of exponential functions,their interaction behaviors are shown by three-dimensional plots and contour plots.展开更多
The Hirota equation can be used to describe the wave propagation of an ultrashort optical field.In this paper,the multi-component Hirota(alias n-Hirota,i.e.n-component third-order nonlinear Schrodinger)equations with ...The Hirota equation can be used to describe the wave propagation of an ultrashort optical field.In this paper,the multi-component Hirota(alias n-Hirota,i.e.n-component third-order nonlinear Schrodinger)equations with mixed non-zero and zero boundary conditions are explored.We employ the multiple roots of the characteristic polynomial related to the Lax pair and modified Darboux transform to find vector semi-rational rogon-soliton solutions(i.e.nonlinear combinations of rogon and soliton solutions).The semi-rational rogon-soliton features can be modulated by the polynomial degree.For the larger solution parameters,the first m(m<n)components with non-zero backgrounds can be decomposed into rational rogons and grey-like solitons,and the last n-m components with zero backgrounds can approach bright-like solitons.Moreover,we analyze the accelerations and curvatures of the quasi-characteristic curves,as well as the variations of accelerations with the distances to judge the interaction intensities between rogons and grey-like solitons.We also find the semi-rational rogon-soliton solutions with ultrahigh amplitudes.In particular,we can also deduce vector semi-rational solitons of the ncomponent complex mKdV equation.These results will be useful to further study the related nonlinear wave phenomena of multi-component physical models with mixed background,and even design the related physical experiments.展开更多
Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-...Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.展开更多
基金supported by the NSF of China under Grant No.12001377,Grant No.11671219 and Grant No.12071304.
文摘N-kink soliton and high-order synchronized breather solutions for potential Kadomtsev-Petviashvili equation are derived by means of the Hirota bilinear method,and the limit process of high-order synchronized breathers are shown.Furthermore,M-lump solutions are also presented by taking the long wave limit.Additionally,a family of semi-rational solutions with elastic collision are generated by taking a long-wave limit of only a part of exponential functions,their interaction behaviors are shown by three-dimensional plots and contour plots.
基金supported by the National Natural Science Foundation of China(Nos.11925108 and 11731014)
文摘The Hirota equation can be used to describe the wave propagation of an ultrashort optical field.In this paper,the multi-component Hirota(alias n-Hirota,i.e.n-component third-order nonlinear Schrodinger)equations with mixed non-zero and zero boundary conditions are explored.We employ the multiple roots of the characteristic polynomial related to the Lax pair and modified Darboux transform to find vector semi-rational rogon-soliton solutions(i.e.nonlinear combinations of rogon and soliton solutions).The semi-rational rogon-soliton features can be modulated by the polynomial degree.For the larger solution parameters,the first m(m<n)components with non-zero backgrounds can be decomposed into rational rogons and grey-like solitons,and the last n-m components with zero backgrounds can approach bright-like solitons.Moreover,we analyze the accelerations and curvatures of the quasi-characteristic curves,as well as the variations of accelerations with the distances to judge the interaction intensities between rogons and grey-like solitons.We also find the semi-rational rogon-soliton solutions with ultrahigh amplitudes.In particular,we can also deduce vector semi-rational solitons of the ncomponent complex mKdV equation.These results will be useful to further study the related nonlinear wave phenomena of multi-component physical models with mixed background,and even design the related physical experiments.
基金Project supported by the BUPT Excellent Ph.D.Students Foundation(Grant No.CX2019201)the National Natural Science Foundation of China(Grant Nos.11772017 and 11805020)+1 种基金the Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),China(Grant No.IPOC:2017ZZ05)the Fundamental Research Funds for the Central Universities of China(Grant No.2011BUPTYB02)。
文摘Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.
