This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain(a nonintegrable system)and compares the simulation results with the theoretical results in fluid(an integrabl...This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain(a nonintegrable system)and compares the simulation results with the theoretical results in fluid(an integrable system).Three stages(the pre-in-phase traveling stage,the central-collision stage,and the post-in-phase traveling stage)are identified to describe the nonlinear interaction processes in the granular chain.The nonlinear scattering effect occurs in the central-collision stage,which decreases the amplitude of the incident solitary waves.Compared with the leading-time phase in the incident and separation collision processes,the lagging-time phase in the separation collision process is smaller.This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage.We next find that the solitary wave amplitude does not influence the immediate space-phase shift in the granular chain.The space-phase shift of the post-in-phase traveling stage is only determined by the measurement position rather than the wave amplitude.The results are reversed in the fluid.An increase in solitary wave amplitude leads to decreased attachment,detachment,and residence times for granular chains and fluid.For the immediate time-phase shift,leading and lagging phenomena appear in the granular chain and the fluid,respectively.These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.展开更多
Objective:To explore the application effect of a doctor-nurse cooperation follow-up model based on an Internet platform in the continuation of care for patients after uro-oncology surgery.Methods:A convenient sampling...Objective:To explore the application effect of a doctor-nurse cooperation follow-up model based on an Internet platform in the continuation of care for patients after uro-oncology surgery.Methods:A convenient sampling method was used to select patients with urinary system tumors who underwent surgery in the Department of Urology in Grade III A general hospital in Shanghai from May to August 2022.Patients who underwent surgery from May to June 2022 were assigned to the control group,and those who underwent surgery from July to August 2022 were assigned to the experimental group.The control group received routine post-discharge nursing health education and telephone follow-up.On the basis of routine discharge guidance,the experimental group implemented the intervention method based on the Internet platform in continuation care.The levels of self-management efficacy,satisfaction,and incidence of unplanned readmission were compared one month after discharge between the two groups.Results:One month after discharge,the self-management efficacy of the experimental group(90.15±7.92)was significantly higher than that of the control group(79.10±7.84),and the patient satisfaction score(97.83±2.32)was significantly higher than that of the control group(90.23±2.58),with statistical significance(P<0.05).Additionally,the incidence of unplanned readmissions within one month after discharge in the experimental group(1.59%)was slightly lower than that in the control group(4.84%).Conclusion:The doctor-nurse cooperation follow-up model based on the Internet platform in continuation care can significantly improve the self-management efficiency of patients after discharge and enhance patient satisfaction,providing a new approach for discharge follow-up of urological tumor patients after surgery.展开更多
We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and the...We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.展开更多
We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems,...We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifthorder mKdV equations are given.展开更多
We introduce a new form of the Painlevé integrable(3+1)-dimensional combined potential Kadomtsev–Petviashvili equation incorporating the B-type Kadomtsev–Petviashvili equation(pKP–BKP equation). We perform the...We introduce a new form of the Painlevé integrable(3+1)-dimensional combined potential Kadomtsev–Petviashvili equation incorporating the B-type Kadomtsev–Petviashvili equation(pKP–BKP equation). We perform the Painlevé analysis to emphasize the complete integrability of this new(3+1)-dimensional combined integrable equation. We formally derive multiple soliton solutions via employing the simplified Hirota bilinear method. Moreover, a variety of lump solutions are determined. We also develop two new(3+1)-dimensional pKP–BKP equations via deleting some terms from the original form of the combined p KP–BKP equation. We emphasize the Painlevé integrability of the newly developed equations, where multiple soliton solutions and lump solutions are derived as well. The derived solutions for all examined models are all depicted through Maple software.展开更多
This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data.We apply this technique to both synthetic and Monte Carlo-generated data.The training sets for neural ...This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data.We apply this technique to both synthetic and Monte Carlo-generated data.The training sets for neural networks are carefully synthesized without“data leakage”.We find that the training set should match the input correlation functions in terms of statistical error properties,such as noise level,noise dependence on imaginary time,and imaginary time-displaced correlations.We have developed a systematic method to synthesize such training datasets.Our improved algorithm outperforms the widely used maximum entropy method in highly noisy situations.As an example,our method successfully extracted the dynamic structure factor of the spin-1/2 Heisenberg chain from quantum Monte Carlo simulations.展开更多
Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solve...Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments.Discontinuous Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the convergence.Here we propose the use of FC in forming a new basis for the DG framework.展开更多
Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with a...Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.展开更多
Continuation method solving forward kinematics problem of parallel robot was discussed. And through a coefficient-parameter continuation method the efficiency and feasibility of continuation method were improved. Usin...Continuation method solving forward kinematics problem of parallel robot was discussed. And through a coefficient-parameter continuation method the efficiency and feasibility of continuation method were improved. Using this method all forward solutions of a new parallel robot model which was put forward lately by Robot Open Laboratory of Science Institute of China were obtained. Therefore it provided the basis of mechanism analysis and real-time control for new model.展开更多
We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads ...We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.展开更多
Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identi...Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction,special cases of this nonlinear super integrable couplings were obtained.展开更多
Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. And its super Hamiltonian structures were established by using super trace identit...Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. And its super Hamiltonian structures were established by using super trace identity. As its reduction, special cases of this nonlinear super integrable coupling were obtained.展开更多
In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi e...In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.展开更多
A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6...A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.展开更多
A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and...A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.展开更多
This paper establishes a new isospectral problem. By making use of the Tu scheme, a new intcgrablc system is obtained. It gives integrable couplings of the system obtained. Finally, the Hamiltonian form of a binary sy...This paper establishes a new isospectral problem. By making use of the Tu scheme, a new intcgrablc system is obtained. It gives integrable couplings of the system obtained. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.展开更多
Based on a kind of non-semisimple Lie algebras, we establish a way to construct nonlinear continuous integrable couplings. Variational identities over the associated loop algebras are used to furnish Hamiltonian struc...Based on a kind of non-semisimple Lie algebras, we establish a way to construct nonlinear continuous integrable couplings. Variational identities over the associated loop algebras are used to furnish Hamiltonian structures of the resulting continuous couplings.As an illustrative example of the scheme is given nonlinear continuous integrable couplings of the Yang hierarchy.展开更多
For the first time,the analytical continuation in the coupling constant method has been combined with the relativistic mean field theory to study the unbound states in spherical nuclei.The 1d_(3/2) neutron state in ^(...For the first time,the analytical continuation in the coupling constant method has been combined with the relativistic mean field theory to study the unbound states in spherical nuclei.The 1d_(3/2) neutron state in ^(16)O and the 2d_(5/2) and 1g_(9/2) neutron states in ^(48)Ca are taken as examples.The calculated energies and widths are compared with available data.展开更多
The equivalence of three (2 + 1)-dimensional soliton equations is proved, and the quite generalsolutionswitha some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, man...The equivalence of three (2 + 1)-dimensional soliton equations is proved, and the quite generalsolutionswitha some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many specialtypes of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutionsare obtained.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11574153)the Foundation of the Ministry of Industry and Information Technology of China(Grant No.TSXK2022D007)。
文摘This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain(a nonintegrable system)and compares the simulation results with the theoretical results in fluid(an integrable system).Three stages(the pre-in-phase traveling stage,the central-collision stage,and the post-in-phase traveling stage)are identified to describe the nonlinear interaction processes in the granular chain.The nonlinear scattering effect occurs in the central-collision stage,which decreases the amplitude of the incident solitary waves.Compared with the leading-time phase in the incident and separation collision processes,the lagging-time phase in the separation collision process is smaller.This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage.We next find that the solitary wave amplitude does not influence the immediate space-phase shift in the granular chain.The space-phase shift of the post-in-phase traveling stage is only determined by the measurement position rather than the wave amplitude.The results are reversed in the fluid.An increase in solitary wave amplitude leads to decreased attachment,detachment,and residence times for granular chains and fluid.For the immediate time-phase shift,leading and lagging phenomena appear in the granular chain and the fluid,respectively.These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.
基金The Project of China Hospital Development Research Institute,Shanghai Jiao Tong University(No.CHDI-2022-B-11)Shanghai Jiao Tong University School of Medicine:Nursing Development Program。
文摘Objective:To explore the application effect of a doctor-nurse cooperation follow-up model based on an Internet platform in the continuation of care for patients after uro-oncology surgery.Methods:A convenient sampling method was used to select patients with urinary system tumors who underwent surgery in the Department of Urology in Grade III A general hospital in Shanghai from May to August 2022.Patients who underwent surgery from May to June 2022 were assigned to the control group,and those who underwent surgery from July to August 2022 were assigned to the experimental group.The control group received routine post-discharge nursing health education and telephone follow-up.On the basis of routine discharge guidance,the experimental group implemented the intervention method based on the Internet platform in continuation care.The levels of self-management efficacy,satisfaction,and incidence of unplanned readmission were compared one month after discharge between the two groups.Results:One month after discharge,the self-management efficacy of the experimental group(90.15±7.92)was significantly higher than that of the control group(79.10±7.84),and the patient satisfaction score(97.83±2.32)was significantly higher than that of the control group(90.23±2.58),with statistical significance(P<0.05).Additionally,the incidence of unplanned readmissions within one month after discharge in the experimental group(1.59%)was slightly lower than that in the control group(4.84%).Conclusion:The doctor-nurse cooperation follow-up model based on the Internet platform in continuation care can significantly improve the self-management efficiency of patients after discharge and enhance patient satisfaction,providing a new approach for discharge follow-up of urological tumor patients after surgery.
文摘We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.
基金supported in part by the National Natural Science Foundation of China (Grant Nos. 11975145, 11972291, and 51771083)the Ministry of Science and Technology of China (Grant No. G2021016032L)the Natural Science Foundation for Colleges and Universities in Jiangsu Province, China (Grant No. 17 KJB 110020)。
文摘We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifthorder mKdV equations are given.
文摘We introduce a new form of the Painlevé integrable(3+1)-dimensional combined potential Kadomtsev–Petviashvili equation incorporating the B-type Kadomtsev–Petviashvili equation(pKP–BKP equation). We perform the Painlevé analysis to emphasize the complete integrability of this new(3+1)-dimensional combined integrable equation. We formally derive multiple soliton solutions via employing the simplified Hirota bilinear method. Moreover, a variety of lump solutions are determined. We also develop two new(3+1)-dimensional pKP–BKP equations via deleting some terms from the original form of the combined p KP–BKP equation. We emphasize the Painlevé integrability of the newly developed equations, where multiple soliton solutions and lump solutions are derived as well. The derived solutions for all examined models are all depicted through Maple software.
基金support from the National Natural Science Foundation of China (Grant Nos. 12274004 and 11888101)
文摘This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data.We apply this technique to both synthetic and Monte Carlo-generated data.The training sets for neural networks are carefully synthesized without“data leakage”.We find that the training set should match the input correlation functions in terms of statistical error properties,such as noise level,noise dependence on imaginary time,and imaginary time-displaced correlations.We have developed a systematic method to synthesize such training datasets.Our improved algorithm outperforms the widely used maximum entropy method in highly noisy situations.As an example,our method successfully extracted the dynamic structure factor of the spin-1/2 Heisenberg chain from quantum Monte Carlo simulations.
文摘Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments.Discontinuous Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the convergence.Here we propose the use of FC in forming a new basis for the DG framework.
文摘Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.
文摘Continuation method solving forward kinematics problem of parallel robot was discussed. And through a coefficient-parameter continuation method the efficiency and feasibility of continuation method were improved. Using this method all forward solutions of a new parallel robot model which was put forward lately by Robot Open Laboratory of Science Institute of China were obtained. Therefore it provided the basis of mechanism analysis and real-time control for new model.
文摘We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.
基金Supported by the Natural Science Foundation of Henan Province(162300410075) the Science and Technology Key Research Foundation of the Education Department of Henan Province(14A110010) the Youth Backbone Teacher Foundationof Shangqiu Normal University(2013GGJS02)
文摘Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction,special cases of this nonlinear super integrable couplings were obtained.
文摘Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. And its super Hamiltonian structures were established by using super trace identity. As its reduction, special cases of this nonlinear super integrable coupling were obtained.
基金supported by NNSFC(11001219,10925104)the Scientific Research Program Funded by Shaanxi Provincial Education Department(2010JK860)
文摘In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.
基金Project supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800)the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806)+2 种基金the Shanghai Leading Academic Discipline Project (Grant No. J50101)the Key Disciplines of Shanghai Municipality (Grant No. S30104)the National Natural Science Foundation of China (Grant Nos. 61072147 and 11071159)
文摘A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.
文摘A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M- dimensional loop algebra ~X is produced. By taking advantage of ~X a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra ~FM of the loop algebra ~X is presented. Based on the ~FM, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.
基金Project supported by the National Natural Science Foundation of China (Grant No 10371070), the Special Funds for Major Specialities of Shanghai Educational Committee and Science Foundation of Educational Committee of Liaoning Province of China (Grant No 2004C057). Xia T Ch would like to express his sincere thanks to Professors Zhang Y F and Guo F K for valuable discussions.
文摘This paper establishes a new isospectral problem. By making use of the Tu scheme, a new intcgrablc system is obtained. It gives integrable couplings of the system obtained. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.
基金Foundation item: Supported by the Natural Science Foundation of China(11271008, 61072147, 11071159) Supported by the First-class Discipline of Universities in Shanghai Supported by the Shanghai University Leading Academic Discipline Project(A13-0101-12-004)
文摘Based on a kind of non-semisimple Lie algebras, we establish a way to construct nonlinear continuous integrable couplings. Variational identities over the associated loop algebras are used to furnish Hamiltonian structures of the resulting continuous couplings.As an illustrative example of the scheme is given nonlinear continuous integrable couplings of the Yang hierarchy.
基金Supported partly by the Major State Basic Research Development Program under Contract Number G2000077407the National Natural Science Foundation of China under Grant Nos.19847002 and 19935030.
文摘For the first time,the analytical continuation in the coupling constant method has been combined with the relativistic mean field theory to study the unbound states in spherical nuclei.The 1d_(3/2) neutron state in ^(16)O and the 2d_(5/2) and 1g_(9/2) neutron states in ^(48)Ca are taken as examples.The calculated energies and widths are compared with available data.
文摘The equivalence of three (2 + 1)-dimensional soliton equations is proved, and the quite generalsolutionswitha some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many specialtypes of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutionsare obtained.