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Symmetries and bilinear equations for the modified BKP hierarchy
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作者 Weici Guo Wenchuang Guan +1 位作者 Shen Wang Jipeng Cheng 《Science China Mathematics》 SCIE CSCD 2023年第7期1529-1544,共16页
The modified Kadomtsev-Petviashvili hierarchy of B type(mBKP hierarchy)and its constrained cases are investigated from the aspect of the Lax formulation.Starting from the Lax equation of the mBKP hierarchy,we firstly ... The modified Kadomtsev-Petviashvili hierarchy of B type(mBKP hierarchy)and its constrained cases are investigated from the aspect of the Lax formulation.Starting from the Lax equation of the mBKP hierarchy,we firstly derive the bilinear equations and show the existence of the tau functions.Then the additional symmetries are constructed,and the corresponding generator is showed to be the squared eigenfunction symmetry.After that,the actions of the additional symmetries on the tau functions are given.At last,the Lax formulation of the constrained mBKP hierarchy is investigated and the corresponding bilinear equations are also discussed. 展开更多
关键词 mBKP hierarchy tau functions additional symmetries squared eigenfunction symmetries constrained mBKP hierarchy bilinear equations
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Soliton molecules for combined mKdV-type bilinear equation
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作者 Zhang-Xuan Zhao Lu-Wei Zhang +1 位作者 Wei Yang Xue-Ping Cheng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2023年第10期1-9,共9页
Starting from the multi-soliton solutions obtained by the Hirota bilinear method,the soli ton molecule structures for the combined mKdV-type bilinear equation(Dt+∑n=1NαnDx2n+1)f*·f=0 are investigated using the ... Starting from the multi-soliton solutions obtained by the Hirota bilinear method,the soli ton molecule structures for the combined mKdV-type bilinear equation(Dt+∑n=1NαnDx2n+1)f*·f=0 are investigated using the velocity resonance mechanism.The two-soliton molecules of the mKdV-35 equation and the three-soliton molecules of the mKdV-357 equation are specifically demonstrated in this paper.With particular selections of the involved arbitrary parameters,especially the wave numbers,it is confirmed that,besides the usual multi-bright soliton molecules,the multi-dark soliton molecules and the mixed multibright-dark soliton molecules can also be obtained.In addition,we discuss the existence of the multi-soliton molecules for the combined mKdV-type bilinear equation with more higher order nonlinear terms and dispersions.The results demonstrate that when N≥4,the combined mKdVtype bilinear equation no longer admits soliton molecules comprising more than four solitons. 展开更多
关键词 soliton molecule combined mKdV-type bilinear equation Hirota bilinear method velocity resonance mechanism
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Symmetries of(2+1)-Dimensional KdV-Ito Equation in the Bilinear Form^1
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作者 PingHAN Department of Physics, Zhoushan Normal College, Zhoushan 316004, ChinaSen-Yue LOU Fudan T.D. Lee Physics Laboratory, Department of PhysicsFudan University, Shanghai 200433, China andDepartment of Physics, Ningbo Normal College, Ningbo 315211, China2 andInstitute of Theoretical Physics, Academia Sinica, Beijing 100080, China(Received July 26, 1993 Revised September 2, 1993) 《浙江海洋学院学报(人文科学版)》 1995年第1期9-14,共6页
A set of symmetries of a generalized (2+l)-dimensional bilinear equation is given by a formal serins formula. There exist four truncated symmetries for the KdV-Ito model. These trun-cated symmetries with four arourary... A set of symmetries of a generalized (2+l)-dimensional bilinear equation is given by a formal serins formula. There exist four truncated symmetries for the KdV-Ito model. These trun-cated symmetries with four arourary functions of time t constitute an infinnite-dirmensional Lin algebra which contains two types of the Virasoro subalgebra. 展开更多
关键词 KDV MATH Dimensional KdV-Ito equation in the bilinear Form^1 Symmetries of FORM
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Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations 被引量:2
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作者 GAI Xiao-Ling GAO Yi-Tian +2 位作者 YU Xin SUN Zhi-Yuan WANG Lei 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第3期473-480,共8页
Kortweg-de Vries (KdV)-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV (GCCKdV) equations are investigated in this paper. Through the d... Kortweg-de Vries (KdV)-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV (GCCKdV) equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonie collisions are presented: (i) two solitons merge and separate from each other periodically; (ii) two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; (iii) two solitons are ftuctuant in the central region of the collision. Propagation features of solitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the a increasing. Amplitude of v increase with the a increasing and decrease with the β increasing. 展开更多
关键词 generalized complex coupled KdV equations bilinear equations two-soliton solutions INTERACTIONS symbolic computation
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Painlevé Property and Exact Solutions to a (2+1) Dimensional KdV-mKdV Equation 被引量:1
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作者 Yuqing Liu Fang Duan Chao Hu 《Journal of Applied Mathematics and Physics》 2015年第6期697-706,共10页
A (2 + 1) dimensional KdV-mKdV equation is proposed and integrability in the sense of Painlevé and some exact solutions are discussed. The B?cklund transformation and bilinear equations are obtained through Painl... A (2 + 1) dimensional KdV-mKdV equation is proposed and integrability in the sense of Painlevé and some exact solutions are discussed. The B?cklund transformation and bilinear equations are obtained through Painlevé analysis. Some exact solutions are deduced by Hirota method and generalized Wronskian method. 展开更多
关键词 (2+1) Dimensional KdV-mKdV equation Painlevé Property Backlund Transformation bilinear equation Wronskian Method
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Two Types of New Solutions to KdV Equation
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作者 GUO Fu-Kui ZHANG Yu-Feng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第4X期577-579,共3页
It is common knowledge that the soliton solutions u(x, t) defined by the bell-shape form is required to satisfy the following condition lira u(x, t) = u(±∞, t) = 0. However, we think that the above conditi... It is common knowledge that the soliton solutions u(x, t) defined by the bell-shape form is required to satisfy the following condition lira u(x, t) = u(±∞, t) = 0. However, we think that the above condition can be modified as lim u(x, t) = u(±∞, t)^x→ = c, where c is a constant, which is called as a stationary height of u(x, t) in the present paper.^x→∞ If u(x, t) is a bell-shape solitary solution, then the stationary height of each solitary wave is just c. Under the constraint c = 0, all the solitary waves coming from the N-bell-shape-sollton solutions of the KdV equation are the same-oriented travelling. A new type of N-soliton solution with the bell shape is obtained in the paper, whose stationary height is an arbitrary constant c. Taking c ≥ 0, the resulting solitary wave is bound to be the same-oriented travelling. Otherwise, the resulting solitary wave may travel at the same orientation, and also at the opposite orientation. In addition, another type of singular rational travelling solution to the KdV equation is worked out. 展开更多
关键词 soliton solution Hirota method bilinear differential equation
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A Modified Homogeneous Balance Method and Its Applications 被引量:1
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作者 刘春平 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第8期223-227,共5页
A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbala... A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations. 展开更多
关键词 homogeneous balance method bilinear equation generalized Boussinesq equation KP equation mKdV equation
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Lump Solution of (2+1)-Dimensional Boussinesq Equation 被引量:5
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作者 马彩虹 邓爱平 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第5期546-552,共7页
A class of lump solutions of(2+1)-dimensional Boussinesq equation are obtained with the help of Maple by using Hirota bilinear method.Some contour plots with different determinant values are sequentially made to show ... A class of lump solutions of(2+1)-dimensional Boussinesq equation are obtained with the help of Maple by using Hirota bilinear method.Some contour plots with different determinant values are sequentially made to show that the corresponding lump solution tends to zero when the determinant approaches zero.The particular lump solutions with specific values of the involved parameters are plotted,as illustrative examples. 展开更多
关键词 lump solution Boussinesq equation exact solution soliton Hirota bilinear method
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Addition Formulae of Discrete KP,q-KP and Two-Component BKP Systems
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作者 高旭 李传忠 贺劲松 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第4期410-422,共13页
In this paper,we construct the addition formulae for several integrable hierarchies,including the discrete KP,the q-deformed KP,the two-component BKP and the D type Drinfeld–Sokolov hierarchies.With the help of the H... In this paper,we construct the addition formulae for several integrable hierarchies,including the discrete KP,the q-deformed KP,the two-component BKP and the D type Drinfeld–Sokolov hierarchies.With the help of the Hirota bilinear equations and τ functions of different kinds of KP hierarchies,we prove that these addition formulae are equivalent to these hierarchies.These studies show that the addition formula in the research of the integrable systems has good universality. 展开更多
关键词 the discrete KP hierarchy the q-deformed KP hierarchy the two-component BKP hierarchy D type Drinfeld–Sokolov hierarchy addition formula Hirota bilinear equations τ function
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