This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous ba...This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.展开更多
A simple algebraic transformation relation of a special type of solution between the (3+1)-dimensionalKadomtsev-petviashvili (KP) equation and the cubic nonlinear Klein Gordon equation (NKG) is established. Us-ing kno...A simple algebraic transformation relation of a special type of solution between the (3+1)-dimensionalKadomtsev-petviashvili (KP) equation and the cubic nonlinear Klein Gordon equation (NKG) is established. Us-ing known solutions of the NKG equation, we can obtain many soliton solutions and periodic solution of the (3+1)-dimensional KP equation.展开更多
Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cann...Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.展开更多
In the previous Letter (Zheng C L and Zhang J F 2002 China.Phys.Lett.19 1399),a localized excitation of the generalized Ablowitz-Kaup-Newell Segur(GAKNS) system was obtained via the standard Painlevé truncated ex...In the previous Letter (Zheng C L and Zhang J F 2002 China.Phys.Lett.19 1399),a localized excitation of the generalized Ablowitz-Kaup-Newell Segur(GAKNS) system was obtained via the standard Painlevé truncated expansion and a special variable separation approach. In this work, starting from a new variable separation approach, a more general variable separation excitation of this system is derived. The abundance of the localized coherent soliton excitations like dromions, lumps,rings, peakons and oscillating soliton excitations can be constructed by introducing appropriate lower-dimensional soliton patterns. Meanwhile we discuss two kinds of interactions of solitons. One is the interaction between the travelling peakon type soliton excitations,which is not completely elastic. The other is the interaction between the travelling ring type soliton excitations, which is completely elastic.展开更多
Using the standard truncated Painlevé analysis approach, we have obtained some new special types of multisoliton solutions of a (2+ 1)-dimensionM integrable model, the modified Kadomtsev-Petviashvili (mKP) equation.
By using the extended Hirota's method, the N-soliton-like solution of the Ito equation is obtained. Furthermore, we also investigate the soliton-like solution interaction and find singularity.
From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2+1)-dimensional long-wave-short-wav...From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The completely elastic and non-elastic interactive behavior between the dromion and compacton, dromion and peakon, as well as between peakon and compacton are investigated. The novel features exhibited by these new structures are revealed for the first time.展开更多
By the use of the extended homogenous balance method,the B(?)cklund transformation for a (2+1)- dimensional integrable model,the(2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation,is obtained,and then the NNV equ...By the use of the extended homogenous balance method,the B(?)cklund transformation for a (2+1)- dimensional integrable model,the(2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation,is obtained,and then the NNV equation is transformed into three equations of linear,bilinear,and tri-linear forms,respectively.From the above three equations,a rather general variable separation solution of the model is obtained.Three novel class localized structures of the model are founded by the entrance of two variable-separated arbitrary functions.展开更多
Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained...Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.展开更多
A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we c...A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite general solution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.展开更多
Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave soluti...Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave solutions of certain nonlinear partial differential models.Now we can further extend the new algorithm to other nonlinear differential-different models.展开更多
The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partial differential equation. Applying the B?cklund transformation and introducing the arbitrary...The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partial differential equation. Applying the B?cklund transformation and introducing the arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types of solutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functions appropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the number of the peaks.展开更多
A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+1)-dimensional nonlinear models related to Schr6dinger equation by the entranc...A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.展开更多
A new class of support vector machine, nil-support vector machine, isdiscussed which can handle both classification and regression. We focus on nu-support vector machineregression and use it for phase space prediction...A new class of support vector machine, nil-support vector machine, isdiscussed which can handle both classification and regression. We focus on nu-support vector machineregression and use it for phase space prediction of chaotic time series. The effectiveness of themethod is demonstrated by applying it to the Henon map. This study also compares nu-support vectormachine with back propagation (BP) networks in order to better evaluate the performance of theproposed methods. The experimental results show that the nu-support vector machine regressionobtains lower root mean squared error than the BP networks and provides an accurate chaotic timeseries prediction. These results can be attributable to the fact that nu-support vector machineimplements the structural risk minimization principle and this leads to better generalization thanthe BP networks.展开更多
By using the generalized tanh-function method, we find bright and dark solitary wave solutions to an extended nonlinear Schrodinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonli...By using the generalized tanh-function method, we find bright and dark solitary wave solutions to an extended nonlinear Schrodinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonlinear terms, describing the propagation of extremely short pulses. At the same time, we also obtained other types of exact solutions.展开更多
Using the standard truncated Painlev? analysis, we can obtain a B?cklund transformation of the (3+1)-dimensional Nizhnik?Novikov?Veselov (NNV) equation and get some (3+1)-dimensional single-, two- and three-soliton so...Using the standard truncated Painlev? analysis, we can obtain a B?cklund transformation of the (3+1)-dimensional Nizhnik?Novikov?Veselov (NNV) equation and get some (3+1)-dimensional single-, two- and three-soliton solutions and some new types of multisoliton solutions of the (3+1)-dimensional NNV system from the B?cklund transformation and the trivial vacuum solution.展开更多
We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this...We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.展开更多
Starting from the variable separation solution obtained by using the extended homogenous balance method,a new class of combined structures, such as multi-peakon and multi-dromion solution, multi-compacton and multidro...Starting from the variable separation solution obtained by using the extended homogenous balance method,a new class of combined structures, such as multi-peakon and multi-dromion solution, multi-compacton and multidromion solution, multi-peakon and multi-compacton solution, for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are found by selecting appropriate functions. These new structures exhibit novel interaction features. Their interaction behavior is very similar to the completely nonelastic collisions between two classical particles.展开更多
In ordet to maintain the dependability of system and meet the functional needof users dtsire, this paper introduces a survivability mechanism into embedded real-time system,and proposes a general comprehensive, approa...In ordet to maintain the dependability of system and meet the functional needof users dtsire, this paper introduces a survivability mechanism into embedded real-time system,and proposes a general comprehensive, approach based on a rigorous definition of survivability. Thisapproach permits a trade-off between the function and the cost of system development. It emphasizesthe ultradependable implementation of crucial function without demanding that of entire system.展开更多
A new dinuclear copper(II) complex ([Cu(C12H17N2O)(N3)]2, C24H34Cu2N10O2) has been synthesized and characterized by X-ray structure determination. It crystallizes in the monoclinic system, space group P21/c with a =...A new dinuclear copper(II) complex ([Cu(C12H17N2O)(N3)]2, C24H34Cu2N10O2) has been synthesized and characterized by X-ray structure determination. It crystallizes in the monoclinic system, space group P21/c with a = 18.529(4), b = 10.933(2), c = 14.534(3) ?, β = 111.07(3)°, V = 2748(1) ?3, Z = 4, Mr = 621.69, F(000) = 1288, Dc = 1.503 g/cm3 and μ(MoKα) = 1.590 mm?1. The structure was refined to R = 0.0647 and wR = 0.1846 for 4406 observed reflections (I > 2σ(I)). The asymmetric unit comprises two halfmolecules. The complex is a centrosymmetric dimmer in which the copper atoms are penta-coordinated by three coordination atoms from the corresponding tridentate Schiff base ligand and two bridging azide anions. The Cu(II)…Cu(II) average distance is 3.350(1) ?.展开更多
文摘This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.
文摘A simple algebraic transformation relation of a special type of solution between the (3+1)-dimensionalKadomtsev-petviashvili (KP) equation and the cubic nonlinear Klein Gordon equation (NKG) is established. Us-ing known solutions of the NKG equation, we can obtain many soliton solutions and periodic solution of the (3+1)-dimensional KP equation.
基金国家杰出青年科学基金，the Research Fund for the Doctoral Program of Higher Education of China
文摘Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.
文摘In the previous Letter (Zheng C L and Zhang J F 2002 China.Phys.Lett.19 1399),a localized excitation of the generalized Ablowitz-Kaup-Newell Segur(GAKNS) system was obtained via the standard Painlevé truncated expansion and a special variable separation approach. In this work, starting from a new variable separation approach, a more general variable separation excitation of this system is derived. The abundance of the localized coherent soliton excitations like dromions, lumps,rings, peakons and oscillating soliton excitations can be constructed by introducing appropriate lower-dimensional soliton patterns. Meanwhile we discuss two kinds of interactions of solitons. One is the interaction between the travelling peakon type soliton excitations,which is not completely elastic. The other is the interaction between the travelling ring type soliton excitations, which is completely elastic.
文摘Using the standard truncated Painlevé analysis approach, we have obtained some new special types of multisoliton solutions of a (2+ 1)-dimensionM integrable model, the modified Kadomtsev-Petviashvili (mKP) equation.
文摘By using the extended Hirota's method, the N-soliton-like solution of the Ito equation is obtained. Furthermore, we also investigate the soliton-like solution interaction and find singularity.
文摘From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The completely elastic and non-elastic interactive behavior between the dromion and compacton, dromion and peakon, as well as between peakon and compacton are investigated. The novel features exhibited by these new structures are revealed for the first time.
文摘By the use of the extended homogenous balance method,the B(?)cklund transformation for a (2+1)- dimensional integrable model,the(2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation,is obtained,and then the NNV equation is transformed into three equations of linear,bilinear,and tri-linear forms,respectively.From the above three equations,a rather general variable separation solution of the model is obtained.Three novel class localized structures of the model are founded by the entrance of two variable-separated arbitrary functions.
文摘Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.
文摘A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite general solution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.
文摘Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave solutions of certain nonlinear partial differential models.Now we can further extend the new algorithm to other nonlinear differential-different models.
文摘The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partial differential equation. Applying the B?cklund transformation and introducing the arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types of solutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functions appropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the number of the peaks.
文摘A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.
文摘A new class of support vector machine, nil-support vector machine, isdiscussed which can handle both classification and regression. We focus on nu-support vector machineregression and use it for phase space prediction of chaotic time series. The effectiveness of themethod is demonstrated by applying it to the Henon map. This study also compares nu-support vectormachine with back propagation (BP) networks in order to better evaluate the performance of theproposed methods. The experimental results show that the nu-support vector machine regressionobtains lower root mean squared error than the BP networks and provides an accurate chaotic timeseries prediction. These results can be attributable to the fact that nu-support vector machineimplements the structural risk minimization principle and this leads to better generalization thanthe BP networks.
文摘By using the generalized tanh-function method, we find bright and dark solitary wave solutions to an extended nonlinear Schrodinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonlinear terms, describing the propagation of extremely short pulses. At the same time, we also obtained other types of exact solutions.
文摘Using the standard truncated Painlev? analysis, we can obtain a B?cklund transformation of the (3+1)-dimensional Nizhnik?Novikov?Veselov (NNV) equation and get some (3+1)-dimensional single-, two- and three-soliton solutions and some new types of multisoliton solutions of the (3+1)-dimensional NNV system from the B?cklund transformation and the trivial vacuum solution.
文摘We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.
文摘Starting from the variable separation solution obtained by using the extended homogenous balance method,a new class of combined structures, such as multi-peakon and multi-dromion solution, multi-compacton and multidromion solution, multi-peakon and multi-compacton solution, for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are found by selecting appropriate functions. These new structures exhibit novel interaction features. Their interaction behavior is very similar to the completely nonelastic collisions between two classical particles.
文摘In ordet to maintain the dependability of system and meet the functional needof users dtsire, this paper introduces a survivability mechanism into embedded real-time system,and proposes a general comprehensive, approach based on a rigorous definition of survivability. Thisapproach permits a trade-off between the function and the cost of system development. It emphasizesthe ultradependable implementation of crucial function without demanding that of entire system.
文摘A new dinuclear copper(II) complex ([Cu(C12H17N2O)(N3)]2, C24H34Cu2N10O2) has been synthesized and characterized by X-ray structure determination. It crystallizes in the monoclinic system, space group P21/c with a = 18.529(4), b = 10.933(2), c = 14.534(3) ?, β = 111.07(3)°, V = 2748(1) ?3, Z = 4, Mr = 621.69, F(000) = 1288, Dc = 1.503 g/cm3 and μ(MoKα) = 1.590 mm?1. The structure was refined to R = 0.0647 and wR = 0.1846 for 4406 observed reflections (I > 2σ(I)). The asymmetric unit comprises two halfmolecules. The complex is a centrosymmetric dimmer in which the copper atoms are penta-coordinated by three coordination atoms from the corresponding tridentate Schiff base ligand and two bridging azide anions. The Cu(II)…Cu(II) average distance is 3.350(1) ?.
