In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asympt...In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asymptotic behaviors of the Jost solutions as|λ|→∞andλ→0 are given.Considering that the scattering coefficients have simple zeros,the matrix RH problem,reconstruction formulas and corresponding trace formulas are also derived.Further,the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants.The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed.In particular,the asymptotic expressions of two-soliton solutions as|t|→∞are obtained,which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts.In addition,three types of bounded states for two-soliton solutions are presented with certain parametric conditions.展开更多
The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate fr...The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.展开更多
In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring model.Themas...In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring model.Themassive Thirring model consists of a system of two nonlinear complex differential equations,and it plays a dynamic role in quantum field theory.The fractional derivative is considered in the Caputo sense,and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique.In order to illustrate and validate the efficiency of the future technique,we analyzed projected phenomena in terms of fractional order.Moreover,the behaviour of the obtained solution has been captured for diverse fractional order.The obtained results elucidate that the projected technique is easy to implement and very effective to analyze the behaviour of complex nonlinear differential equations of fractional order arising in the connected areas of science and engineering.展开更多
In this paper,the long-time dynamics of the massive Thirring model are investigated.First,the nonlinear steepest descent method for the Riemann-Hilbert problem is explored to obtain the soliton resolution of the solut...In this paper,the long-time dynamics of the massive Thirring model are investigated.First,the nonlinear steepest descent method for the Riemann-Hilbert problem is explored to obtain the soliton resolution of the solutions to the massive Thirring model with initial data in certain weighted-Sobolev spaces.Second,the asymptotic stability of multi-solitons to the massive Thirring model is established as a conclusion.The main difficulty in studying the massive Thirring model through the inverse scattering method is that the corresponding Lax pair exhibits singularities at the origin and infinity.We overcome the difficulty by introducing a pair of gauge transforms that effectively separate the singularities and exploring the delicate analysis of the inverse scattering method.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12475003 and11705284)by the Natural Science Foundation of Beijing Municipality(Grant Nos.1232022 and 1212007)。
文摘In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asymptotic behaviors of the Jost solutions as|λ|→∞andλ→0 are given.Considering that the scattering coefficients have simple zeros,the matrix RH problem,reconstruction formulas and corresponding trace formulas are also derived.Further,the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants.The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed.In particular,the asymptotic expressions of two-soliton solutions as|t|→∞are obtained,which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts.In addition,three types of bounded states for two-soliton solutions are presented with certain parametric conditions.
基金the Natural Science Foundation of Sichuan Normal University
文摘The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.
文摘In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring model.Themassive Thirring model consists of a system of two nonlinear complex differential equations,and it plays a dynamic role in quantum field theory.The fractional derivative is considered in the Caputo sense,and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique.In order to illustrate and validate the efficiency of the future technique,we analyzed projected phenomena in terms of fractional order.Moreover,the behaviour of the obtained solution has been captured for diverse fractional order.The obtained results elucidate that the projected technique is easy to implement and very effective to analyze the behaviour of complex nonlinear differential equations of fractional order arising in the connected areas of science and engineering.
基金supported by National Natural Science Foundation of China(Grant No.12431008)K.C.Wong Magna Fund in Ningbo University+1 种基金supported by National NaturalScience Foundation of China(Grant No.12201605)supported by National Natural ScienceFoundation of China(Grant Nos.12431008 and 11971251)。
文摘In this paper,the long-time dynamics of the massive Thirring model are investigated.First,the nonlinear steepest descent method for the Riemann-Hilbert problem is explored to obtain the soliton resolution of the solutions to the massive Thirring model with initial data in certain weighted-Sobolev spaces.Second,the asymptotic stability of multi-solitons to the massive Thirring model is established as a conclusion.The main difficulty in studying the massive Thirring model through the inverse scattering method is that the corresponding Lax pair exhibits singularities at the origin and infinity.We overcome the difficulty by introducing a pair of gauge transforms that effectively separate the singularities and exploring the delicate analysis of the inverse scattering method.
