This paper studies the non-homogeneous generalized Riemann-Hilbert(RH)problems involving two unknown functions.Using the uniformization theorem,such problems are transformed into the case of homogeneous type.By the th...This paper studies the non-homogeneous generalized Riemann-Hilbert(RH)problems involving two unknown functions.Using the uniformization theorem,such problems are transformed into the case of homogeneous type.By the theory of classical boundary value problems,we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains,and analyze the conditions of solvability and properties of solutions in various domains.展开更多
We study the complex Sharma-Tasso-Olver equation using the Riemann-Hilbert approach.The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem ...We study the complex Sharma-Tasso-Olver equation using the Riemann-Hilbert approach.The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem of the Lax pair.Subsequently,in the case that the Riemann-Hilbert problem is irregular,the N-soliton solutions of the equation can be deduced.In addition,the three-dimensional graphic of the soliton solutions and wave propagation image are graphically depicted and further discussed.展开更多
This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the ...This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.展开更多
The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses...The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.展开更多
We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis main...We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11971015).
文摘This paper studies the non-homogeneous generalized Riemann-Hilbert(RH)problems involving two unknown functions.Using the uniformization theorem,such problems are transformed into the case of homogeneous type.By the theory of classical boundary value problems,we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains,and analyze the conditions of solvability and properties of solutions in various domains.
基金Project supported by the National Natural Science Foundation of China(Grant No.11975145)the Program for Science&Technology Innovation Talents in Universities of Henan Province,China(Grant No.22HASTIT019)+2 种基金the Natural Science Foundation of Henan,China(Grant No.202300410524)the Science and Technique Project of Henan,China(Grant No.212102310397)the Academic Degrees&Graduate Education Reform Project of Henan Province,China(Grant No.2021SJGLX219Y)。
文摘We study the complex Sharma-Tasso-Olver equation using the Riemann-Hilbert approach.The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem of the Lax pair.Subsequently,in the case that the Riemann-Hilbert problem is irregular,the N-soliton solutions of the equation can be deduced.In addition,the three-dimensional graphic of the soliton solutions and wave propagation image are graphically depicted and further discussed.
基金supported by the Natural Science Foundation of Hebei Province,China (Grant No.A2021502004)the Fundamental Research Funds for the Central Universities (Grant No.2024MS126).
文摘This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.
