We concentrate on the inverse scattering transformation for the Sasa-Satsuma equation with 3×3 matrix spectrum problem and a nonzero boundary condition. To circumvent the multi-value of eigenvalues, we introduce ...We concentrate on the inverse scattering transformation for the Sasa-Satsuma equation with 3×3 matrix spectrum problem and a nonzero boundary condition. To circumvent the multi-value of eigenvalues, we introduce a suitable two-sheet Riemann surface to map the original spectral parameter k into a single-valued parameter z. The analyticity of the Jost eigenfunctions and scattering coefficients of the Lax pair for the Sasa-Satsuma equation are analyzed in detail. According to the analyticity of the eigenfunctions and the scattering coefficients, the z-complex plane is divided into four analytic regions of D_(j) : j = 1, 2, 3, 4. Since the second column of Jost eigenfunctions is analytic in D_(j), but in the upper-half or lowerhalf plane, we introduce certain auxiliary eigenfunctions which are necessary for deriving the analytic eigenfunctions in Dj. We find that the eigenfunctions, the scattering coefficients and the auxiliary eigenfunctions all possess three kinds of symmetries;these characterize the distribution of the discrete spectrum. The asymptotic behaviors of eigenfunctions, auxiliary eigenfunctions and scattering coefficients are also systematically derived. Then a matrix Riemann-Hilbert problem with four kinds of jump conditions associated with the problem of nonzero asymptotic boundary conditions is established, from this N-soliton solutions are obtained via the corresponding reconstruction formulae. The reflectionless soliton solutions are explicitly given. As an application of the N-soliton formula, we present three kinds of single-soliton solutions according to the distribution of discrete spectrum.展开更多
The Sasa-satsuma(SS)dynamical equation interpret propagation of ultra-short and femto-second pulses in optical fibers.This dynamical model has important physical significance.In this article,two mathematical technique...The Sasa-satsuma(SS)dynamical equation interpret propagation of ultra-short and femto-second pulses in optical fibers.This dynamical model has important physical significance.In this article,two mathematical techniques namely,improved F-expansion and improved aux-iliary methods are utilized to construct the several types of solitons such as dark soliton,bright soliton,periodic soliton,Elliptic function and solitary waves solutions of Sasa-satsuma dynamical equation.These results have imperative applications in sciences and other fields,and construc-tive to recognize the physical structure of this complex dynamical model.The computing work and obtained results show the infuence and effectiveness of current methods.展开更多
This work proposes the construction of a prototype of pulse-kink hybrid solitary waves with a strong Kink dosage of the Sasa-Satsuma equation which describes the dynamics of the wave propagating in an optical fiber wh...This work proposes the construction of a prototype of pulse-kink hybrid solitary waves with a strong Kink dosage of the Sasa-Satsuma equation which describes the dynamics of the wave propagating in an optical fiber where the stimulated Raman scattering effect is bethinking during modeling. The ultimate goal of this work is to propose a plateful of solutions likely to serve as signals during studies on computer or laboratory propagation studies. The resolution of such an equation is not always the easiest thing, and we used the Bogning-Djeumen Tchaho-Kofané method extended to the implicit functions of Bogning to obtain the results. The flexibility of the iB-functions made it possible to deduce the trigonometric solutions, from the obtained solitary wave solutions with a hyperbolic analytical sequence of the studied Sasa-Satsuma equation. A better appreciation of the nature of the solutions obtained is made through the profiles of some solutions obtained during the different analyses.展开更多
In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmeth...In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.展开更多
The research of rogue waves is an advanced field which has important practical and theoretical significances in mathematics,physics,biological fluid mechanics,oceanography,etc.Using the reductive perturbation theory a...The research of rogue waves is an advanced field which has important practical and theoretical significances in mathematics,physics,biological fluid mechanics,oceanography,etc.Using the reductive perturbation theory and long wave approximation,the equations governing the movement of blood vessel walls and the flow of blood are transformed into high-order nonlinear Schrodinger(NLS)equations with variable coefficients.The third-order nonlinear Schrodinger equation is degenerated into a completely integrable Sasa–Satsuma equation(SSE)whose solutions can be used to approximately simulate the real rogue waves in the vessels.For the first time,we discuss the conditions for generating rogue waves in the blood vessels and effects of some physiological parameters on the rogue waves.Based on the traveling wave solutions of the fourth-order nonlinear Schrodinger equation,we analyze the effects of the higher order terms and the initial deformations of the blood vessel on the wave propagation and the displacement of the tube wall.Our results reveal that the amplitude of the rogue waves are proportional to the initial stretching ratio of the tube.The high-order nonlinear and dispersion terms lead to the distortion of the wave,while the initial deformation of the tube wall will influence the wave amplitude and wave steepness.展开更多
In this work,we study the Riemann–Hilbert problem and the soliton solutions for a nonlocal Sasa–Satsuma equation with reverse-time type,which is deduced from a reduction of the coupled Sasa–Satsuma system.Since the...In this work,we study the Riemann–Hilbert problem and the soliton solutions for a nonlocal Sasa–Satsuma equation with reverse-time type,which is deduced from a reduction of the coupled Sasa–Satsuma system.Since the coupled Sasa–Satsuma system can describe the dynamic behaviors of two ultrashort pulse envelopes in birefringent fiber,our equation presented here has great physical applications.The classification of soliton solutions is studied in this nonlocal model by considering an inverse scattering transform to the Riemann–Hilbert problem.Simultaneously,we find that the symmetry relations of discrete data in the special nonlocal model are very complicated.Especially,the eigenvectors in the scattering data are determined by the number and location of eigenvalues.Furthermore,multi-soliton solutions are not a simple nonlinear superposition of multiple single-solitons.They exhibit some novel dynamics of solitons,including meandering and sudden position shifts.Also,they have the bound state of multi-soliton entanglement and its interaction with solitons.展开更多
The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–...The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. Then the Riemann–Hilbert problem corresponding to the reflection-less case is solved.As applications, multi-soliton solutions are obtained for the coupled Sasa–Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons.展开更多
基金supported by the National Natural Science Foundation of China(12175069 and 12235007)the Science and Technology Commission of Shanghai Municipality (21JC1402500 and 22DZ2229014)。
文摘We concentrate on the inverse scattering transformation for the Sasa-Satsuma equation with 3×3 matrix spectrum problem and a nonzero boundary condition. To circumvent the multi-value of eigenvalues, we introduce a suitable two-sheet Riemann surface to map the original spectral parameter k into a single-valued parameter z. The analyticity of the Jost eigenfunctions and scattering coefficients of the Lax pair for the Sasa-Satsuma equation are analyzed in detail. According to the analyticity of the eigenfunctions and the scattering coefficients, the z-complex plane is divided into four analytic regions of D_(j) : j = 1, 2, 3, 4. Since the second column of Jost eigenfunctions is analytic in D_(j), but in the upper-half or lowerhalf plane, we introduce certain auxiliary eigenfunctions which are necessary for deriving the analytic eigenfunctions in Dj. We find that the eigenfunctions, the scattering coefficients and the auxiliary eigenfunctions all possess three kinds of symmetries;these characterize the distribution of the discrete spectrum. The asymptotic behaviors of eigenfunctions, auxiliary eigenfunctions and scattering coefficients are also systematically derived. Then a matrix Riemann-Hilbert problem with four kinds of jump conditions associated with the problem of nonzero asymptotic boundary conditions is established, from this N-soliton solutions are obtained via the corresponding reconstruction formulae. The reflectionless soliton solutions are explicitly given. As an application of the N-soliton formula, we present three kinds of single-soliton solutions according to the distribution of discrete spectrum.
文摘The Sasa-satsuma(SS)dynamical equation interpret propagation of ultra-short and femto-second pulses in optical fibers.This dynamical model has important physical significance.In this article,two mathematical techniques namely,improved F-expansion and improved aux-iliary methods are utilized to construct the several types of solitons such as dark soliton,bright soliton,periodic soliton,Elliptic function and solitary waves solutions of Sasa-satsuma dynamical equation.These results have imperative applications in sciences and other fields,and construc-tive to recognize the physical structure of this complex dynamical model.The computing work and obtained results show the infuence and effectiveness of current methods.
文摘This work proposes the construction of a prototype of pulse-kink hybrid solitary waves with a strong Kink dosage of the Sasa-Satsuma equation which describes the dynamics of the wave propagating in an optical fiber where the stimulated Raman scattering effect is bethinking during modeling. The ultimate goal of this work is to propose a plateful of solutions likely to serve as signals during studies on computer or laboratory propagation studies. The resolution of such an equation is not always the easiest thing, and we used the Bogning-Djeumen Tchaho-Kofané method extended to the implicit functions of Bogning to obtain the results. The flexibility of the iB-functions made it possible to deduce the trigonometric solutions, from the obtained solitary wave solutions with a hyperbolic analytical sequence of the studied Sasa-Satsuma equation. A better appreciation of the nature of the solutions obtained is made through the profiles of some solutions obtained during the different analyses.
基金Supported by the National Natural Science Foundation of China under Grant No. 10735030Shanghai Leading Academic Discipline Project under Grant No. B412+2 种基金National Natural Science Foundation of China under Grant No. 90718041Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT0734K.C. Wong Magna Fund in Ningbo University
文摘In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.
基金Project supported by the National Natural Science Foundation of China(Grant No.11975143)Nature Science Foundation of Shandong Province of China(Grant No.ZR2018MA017)+1 种基金the Taishan Scholars Program of Shandong Province,China(Grant No.ts20190936)the Shandong University of Science and Technology Research Fund(Grant No.2015TDJH102).
文摘The research of rogue waves is an advanced field which has important practical and theoretical significances in mathematics,physics,biological fluid mechanics,oceanography,etc.Using the reductive perturbation theory and long wave approximation,the equations governing the movement of blood vessel walls and the flow of blood are transformed into high-order nonlinear Schrodinger(NLS)equations with variable coefficients.The third-order nonlinear Schrodinger equation is degenerated into a completely integrable Sasa–Satsuma equation(SSE)whose solutions can be used to approximately simulate the real rogue waves in the vessels.For the first time,we discuss the conditions for generating rogue waves in the blood vessels and effects of some physiological parameters on the rogue waves.Based on the traveling wave solutions of the fourth-order nonlinear Schrodinger equation,we analyze the effects of the higher order terms and the initial deformations of the blood vessel on the wave propagation and the displacement of the tube wall.Our results reveal that the amplitude of the rogue waves are proportional to the initial stretching ratio of the tube.The high-order nonlinear and dispersion terms lead to the distortion of the wave,while the initial deformation of the tube wall will influence the wave amplitude and wave steepness.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.2022FRFK060015)supported by the China Postdoctoral Science Foundation(Grant No.2022M710969)the National Natural Science Foundation of China(No.12101159)。
文摘In this work,we study the Riemann–Hilbert problem and the soliton solutions for a nonlocal Sasa–Satsuma equation with reverse-time type,which is deduced from a reduction of the coupled Sasa–Satsuma system.Since the coupled Sasa–Satsuma system can describe the dynamic behaviors of two ultrashort pulse envelopes in birefringent fiber,our equation presented here has great physical applications.The classification of soliton solutions is studied in this nonlocal model by considering an inverse scattering transform to the Riemann–Hilbert problem.Simultaneously,we find that the symmetry relations of discrete data in the special nonlocal model are very complicated.Especially,the eigenvectors in the scattering data are determined by the number and location of eigenvalues.Furthermore,multi-soliton solutions are not a simple nonlinear superposition of multiple single-solitons.They exhibit some novel dynamics of solitons,including meandering and sudden position shifts.Also,they have the bound state of multi-soliton entanglement and its interaction with solitons.
基金Supported by the National Natural Science Foundation of China under Project Nos.11331008 and 11171312the Collaborative Innovation Center for Aviation Economy Development of Henan Province
文摘The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. Then the Riemann–Hilbert problem corresponding to the reflection-less case is solved.As applications, multi-soliton solutions are obtained for the coupled Sasa–Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons.
