With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phen...With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.展开更多
This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton）...This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton） solutions and multiple-singular-kink （soliton） solutions are derived for the two equations.展开更多
The mixed AKNS nonlinear evolution equation in equation, which contains an isospectral term the AKNS system. So searching for its exact and a nonisospectral term, is an important solutions is vital both for the AKNS s...The mixed AKNS nonlinear evolution equation in equation, which contains an isospectral term the AKNS system. So searching for its exact and a nonisospectral term, is an important solutions is vital both for the AKNS system and in mathematical sense. In this paper, the corresponding Lax pair was given, the bilinear forms of the mixed AKNS equation were obtained through introducing the transformation of dependent variables. By using Hirota＇s bilinear method, the N-soliton solutions were obtained.展开更多
Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform s...Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.展开更多
In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are ...In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are also proposed/or this model.展开更多
Periodic solitons are studied in dispersion decreasing fibers with a cosine profile. The variable-coefficient nonlinear Schrrdinger equation, which can be used to describe the propagation of solitons, is investigated ...Periodic solitons are studied in dispersion decreasing fibers with a cosine profile. The variable-coefficient nonlinear Schrrdinger equation, which can be used to describe the propagation of solitons, is investigated analytically. Analytic soli- ton solutions for this equation are derived with the Hirota＇s bilinear method. Using the soliton solutions, we obtain periodic solitons, and analyze the soliton characteristics. Influences of physical parameters on periodic solitons are discussed. The presented results can be used in optical communication systems and fiber lasers.展开更多
In this letter we consider a limit symmetry of the modified KdV equation and its application. The similarity reduction leads to limit solutions of the modified KdV equation. Besides, a modified KdV equation with new s...In this letter we consider a limit symmetry of the modified KdV equation and its application. The similarity reduction leads to limit solutions of the modified KdV equation. Besides, a modified KdV equation with new self-consistent sources is obtained and its solutions are derived.展开更多
With the rapid development of communication technology,optical fiber communication has become a key research area in communications.When there are two signals in the optical fiber,the transmission of them can be abstr...With the rapid development of communication technology,optical fiber communication has become a key research area in communications.When there are two signals in the optical fiber,the transmission of them can be abstracted as a high-order coupled nonlinear Schr¨odinger system.In this paper,by using the Hirota’s method,we construct the bilinear forms,and study the analytical solution of three solitons in the case of focusing interactions.In addition,by adjusting different wave numbers for phase control,we further discuss the influence of wave numbers on soliton transmissions.It is verified that wave numbers k_(11),k_(21),k_(31),k_(22),and k_(32)can control the fusion and fission of solitons.The results are beneficial to the study of all-optical switches and fiber lasers in nonlinear optics.展开更多
Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources （corresponding to λt = -2aA） and its isos...Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources （corresponding to λt = -2aA） and its isospectral counterpart is given, from which exact solutions for the first non-isospectral KdV equation with self-consistent sources is easily listed. Besides, the soliton solutions for the two equations are obtained by means of Hirota＇s method and Wronskian technique, respectively. Meanwhile, the dynamical properties for these solutions are investigated.展开更多
Searching for exact solutions to nonlinear evolution equations is a very important and interesting work in non- linear science. In this paper, the modified Boussinesq equation is derived from the modified Gel＇fand-Di...Searching for exact solutions to nonlinear evolution equations is a very important and interesting work in non- linear science. In this paper, the modified Boussinesq equation is derived from the modified Gel＇fand-Dikii （raG-D） system. Furthermore, we study the modified Boussinesq equation by using the bilinear method and Wronskian technique, we obtain the N-soliton solutions to the above equation.展开更多
Using the Hirota's bilinear method,some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation wt+wxxx-6w 2 wx+3 2( w x -1 wy+w-x -1 wz)x=0 and wt+wxxx?6w 2 wx+3 2( wwy+wx-x-...Using the Hirota's bilinear method,some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation wt+wxxx-6w 2 wx+3 2( w x -1 wy+w-x -1 wz)x=0 and wt+wxxx?6w 2 wx+3 2( wwy+wx-x-1 wy)=0 in view of a different treatment.展开更多
In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and c...In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping by the Covariant Prolongation Structure Theory. As a result, we obtain general forms of Lax-Pair representations. In addition, some hidden structural symmetries that govern the dynamics of the GP equation such as SL(2,R), SL(2,C), Virasoro algebra, SU(1,1) and SU(2) are unearthed. Using the Riccati form of the linear eigenvalue problem, infinite number of conservation laws of the GP equation is explicitly constructed and the exact analytical soliton solutions are obtained by employing the simple and straightforward Hirota’s bilinear method.展开更多
文摘With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10871117 and 10571110)
文摘This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton） solutions and multiple-singular-kink （soliton） solutions are derived for the two equations.
基金The project supported by National Natural Science Foundation of China under Grant No. 10371070 and the Special Funds for Major Specialities of Shanghai Education Committee
文摘Bilinear form of the nonisospectral AKNS equation is given. The N-soliton solutions are obtained through Hirota＇s method.
基金Project supported by the National Natural Science Foundation of China （Grant No.40175014）
文摘The mixed AKNS nonlinear evolution equation in equation, which contains an isospectral term the AKNS system. So searching for its exact and a nonisospectral term, is an important solutions is vital both for the AKNS system and in mathematical sense. In this paper, the corresponding Lax pair was given, the bilinear forms of the mixed AKNS equation were obtained through introducing the transformation of dependent variables. By using Hirota＇s bilinear method, the N-soliton solutions were obtained.
文摘Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.
基金The project supported by National Natural Science Foundation of China under Grant No. 90203001, the Fund of the State Key Laboratory of Scientific and Engineering Computing, the Chinese Academy of Sciences, and Hong Kong Research Grant Council under Grant No. HKBU/2016/03P
文摘In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are also proposed/or this model.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61205064,51272202,and 61234006)the Visiting Scholar Funds of the Key Laboratory of Optoelectronic Technology and Systems of Chongqing University(Grant No.0902011812401 5)
文摘Periodic solitons are studied in dispersion decreasing fibers with a cosine profile. The variable-coefficient nonlinear Schrrdinger equation, which can be used to describe the propagation of solitons, is investigated analytically. Analytic soli- ton solutions for this equation are derived with the Hirota＇s bilinear method. Using the soliton solutions, we obtain periodic solitons, and analyze the soliton characteristics. Influences of physical parameters on periodic solitons are discussed. The presented results can be used in optical communication systems and fiber lasers.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10871165 and 10926036the Education Department under Grant No.Y200906909the Natural Science Foundation of under Grant No.Y6100126 of Zhejiang Province
文摘In this letter we consider a limit symmetry of the modified KdV equation and its application. The similarity reduction leads to limit solutions of the modified KdV equation. Besides, a modified KdV equation with new self-consistent sources is obtained and its solutions are derived.
基金supported by the National Natural Science Foundation of China(Grant Nos.11875008,12075034,11975001,and 11975172)the Open Research Fund of State Key Laboratory of Pulsed Power Laser Technology(Grant No.SKL2018KF04)the Fundamental Research Funds for the Central Universities,China(Grant No.2019XD-A09-3)。
文摘With the rapid development of communication technology,optical fiber communication has become a key research area in communications.When there are two signals in the optical fiber,the transmission of them can be abstracted as a high-order coupled nonlinear Schr¨odinger system.In this paper,by using the Hirota’s method,we construct the bilinear forms,and study the analytical solution of three solitons in the case of focusing interactions.In addition,by adjusting different wave numbers for phase control,we further discuss the influence of wave numbers on soliton transmissions.It is verified that wave numbers k_(11),k_(21),k_(31),k_(22),and k_(32)can control the fusion and fission of solitons.The results are beneficial to the study of all-optical switches and fiber lasers in nonlinear optics.
基金supported by the National Natural Science Foundation of China under Grant Nos. 10371070 and 10671121the Foundation for Excellent Postgraduates of Shanghai University under Grant No. Shucx080127
文摘Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources （corresponding to λt = -2aA） and its isospectral counterpart is given, from which exact solutions for the first non-isospectral KdV equation with self-consistent sources is easily listed. Besides, the soliton solutions for the two equations are obtained by means of Hirota＇s method and Wronskian technique, respectively. Meanwhile, the dynamical properties for these solutions are investigated.
基金Project supported by the Science Foundation of Shanghai Municipal Education Commission (Grant No.06AZ081)
文摘Searching for exact solutions to nonlinear evolution equations is a very important and interesting work in non- linear science. In this paper, the modified Boussinesq equation is derived from the modified Gel＇fand-Dikii （raG-D） system. Furthermore, we study the modified Boussinesq equation by using the bilinear method and Wronskian technique, we obtain the N-soliton solutions to the above equation.
基金Supported by the National Natural Science Foundation of China（10871132 11074160） Supported by the National Natura Science Foundation of Henan Province（102300410190 092300410202）
文摘Using the Hirota's bilinear method,some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation wt+wxxx-6w 2 wx+3 2( w x -1 wy+w-x -1 wz)x=0 and wt+wxxx?6w 2 wx+3 2( wwy+wx-x-1 wy)=0 in view of a different treatment.
文摘In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping by the Covariant Prolongation Structure Theory. As a result, we obtain general forms of Lax-Pair representations. In addition, some hidden structural symmetries that govern the dynamics of the GP equation such as SL(2,R), SL(2,C), Virasoro algebra, SU(1,1) and SU(2) are unearthed. Using the Riccati form of the linear eigenvalue problem, infinite number of conservation laws of the GP equation is explicitly constructed and the exact analytical soliton solutions are obtained by employing the simple and straightforward Hirota’s bilinear method.
