期刊文献+
共找到222篇文章
< 1 2 12 >
每页显示 20 50 100
Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation
1
作者 巩乾坤 王惠 王云虎 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期409-416,共8页
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ... This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs. 展开更多
关键词 lump solution rogue wave solution breather wave solution (2+1)-dimensional Hirota-Satsuma-Ito equation
下载PDF
MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A(2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION 被引量:1
2
作者 李岩 姚若侠 夏亚荣 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期80-96,共17页
Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmet... Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic. 展开更多
关键词 (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation soliton molecules velocity resonance nonelastic interaction
下载PDF
Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation
3
作者 Dahe Feng Jibin Li Airen Zhou 《Applied Mathematics》 2024年第8期543-567,共25页
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ... For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation. 展开更多
关键词 (2 + 1)-dimensional Nonlinear Dispersive Boussinesq equation BIFURCATIONS Phase Portrait Analytical Periodic Wave Solution Periodic Cusp Wave Solution
下载PDF
Symmetry Groups and New Exact Solutions to (2+1)-Dimensional Variable Coefficient Canonical Generalized KP Equation 被引量:7
4
作者 ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第3X期405-410,共6页
In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation... In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation. 展开更多
关键词 (2+1)-dimensional variable coefficient canonical generalized KP (VCCGKP) equation modified CK's'direct method symmetry groups Lie symmetry similarity reductions new exact solutions
下载PDF
New periodic wave solutions, localized excitations and their interaction for (2+1)-dimensional Burgers equation 被引量:2
5
作者 马红彩 葛东杰 于耀东 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第12期4344-4353,共10页
Based on the B/icklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a cl... Based on the B/icklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+l)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution). 展开更多
关键词 (2+1)-dimensional burgers equation mutilinear variable separation approach periodicwave solutions localized excitation
下载PDF
Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the(2+1)-dimensional elliptic Toda equation
6
作者 庞福忠 葛根哈斯 赵雪梅 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第5期200-217,共18页
The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions ... The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations. 展开更多
关键词 (2+1)-dimensional elliptic Toda equation resonant interaction lump molecules
下载PDF
Interaction solutions and localized waves to the(2+1)-dimensional Hirota-Satsuma-Ito equation with variable coefficient
7
作者 闫鑫颖 刘锦洲 辛祥鹏 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第7期199-205,共7页
This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé... This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature. 展开更多
关键词 (2+1)-dimensional variable coefficient Hirota-Satsuma-Ito equation Hirota bilinear method long wave limit method N-soliton solutions
下载PDF
Decay Mode Solutions to (2 + 1)-Dimensional Burgers Equation, Cylindrical Burgers Equation and Spherical Burgers Equation 被引量:1
8
作者 Xiangzheng Li Jinliang Zhang Mingliang Wang 《Journal of Applied Mathematics and Physics》 2017年第5期1009-1015,共7页
Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respecti... Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended -expansion method, substituting the solutions obtained into the corresponding transformation of variables, the decay mode solutions of the three (2 + 1)-dimensional equations have been obtained successfully. 展开更多
关键词 DECAY mode Solution (2 + 1)-burgers equation (2 + 1)-Cylindrical burgers equation (2 + 1)-Spherical burgers equation Transformation of Variables Extended (G'/G)-Expansion Method
下载PDF
Chirped Waves for a Generalized (2 + 1)-Dimensional Nonlinear Schrdinger Equation 被引量:1
9
作者 来娴静 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第4期555-559,共5页
The exact chirped soliton-like and quasi-periodic wave solutions of (2 + 1)-dimensional generalized nonlinear Schr6dinger equation including linear and nonlinear gain (loss) with variable coefficients are obtaine... The exact chirped soliton-like and quasi-periodic wave solutions of (2 + 1)-dimensional generalized nonlinear Schr6dinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detalledly in this paper. The form and the behavior of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain (loss). 展开更多
关键词 (2 1)-dimensional nonlinear SchrSdinger equation CHIRP ansatz method soliton-like wave solu- tion qusi-periodic wave solution
下载PDF
On an Auto-Baecklund Transformation for (2+1)-Dimensional VariableCoefficient Generalized KP Equations and Exact Solutions 被引量:1
10
作者 BAICheng-Jie BAICheng-Lin +1 位作者 HANJi-Guang ZHAOHong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第4期677-680,共4页
By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two ... By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two homogeneity equations to be solved, we obtainsome exact solutions containing single solitary waves. 展开更多
关键词 extended homogeneous balance method (2+1)-dimensional variable coefficientgeneralized KP equation auto-Baecklund transformation exact solutions
下载PDF
A Generalized Extended F-Expansion Method and Its Application in (2+1)-Dimensional Dispersive Long Wave Equation 被引量:1
11
作者 HUANG Wen-Hua 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第4X期580-586,共7页
A new generalized extended F-expansion method is presented for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. As an application of this method, we study the (2+1)-dimensio... A new generalized extended F-expansion method is presented for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. As an application of this method, we study the (2+1)-dimensional dispersive long wave equation. With the aid of computerized symbolic computation, a number of doubly periodic wave solutions expressed by various Jacobi elliptic functions are obtained. In the limit cases, the solitary wave solutions are derived as well. 展开更多
关键词 (2+1)-dimensional dispersive long wave equation extended F-expansion Jacobi elliptic function periodic wave solution
下载PDF
New Complexiton Solutions for the(2+1)-dimensional Burgers Equation
12
作者 李文婷 陈续升 张鸿庆 《Northeastern Mathematical Journal》 CSCD 2007年第5期453-463,共11页
In this paper, a new generalized compound Riccati equations rational expansion method (GCRERE) is proposed. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method... In this paper, a new generalized compound Riccati equations rational expansion method (GCRERE) is proposed. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method is not only recover some known solutions, but also find some new and general complexiton solutions. Being concise and straightforward, it is applied to the (2+1)-dimensional Burgers equation. As a result, eight families of new exact analytical solutions for this equation are found. The method can also be applied to other nonlinear partial differential equations. 展开更多
关键词 generalized compound Riccati equations rational expansion method (2+1)-dimensional burgers equation complexiton solution
下载PDF
Multi-symplectic method for the generalized(2+1)-dimensionalKdV-mKdV equation
13
作者 Wei-Peng Hu Zi-Chen Deng +1 位作者 Yu-Yue Qin Wen-Rong Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第3期793-800,共8页
In the present paper, a general solution involv- ing three arbitrary functions for the generalized (2+1)- dimensional KdV-mKdV equation, which is derived from the generalized (1+1)-dimensional KdV-mKdV equa- tio... In the present paper, a general solution involv- ing three arbitrary functions for the generalized (2+1)- dimensional KdV-mKdV equation, which is derived from the generalized (1+1)-dimensional KdV-mKdV equa- tion, is first introduced by means of the Wiess, Tabor, Carnevale (WTC) truncation method. And then multi- symplectic formulations with several conservation laws taken into account are presented for the generalized (2+1)- dimensional KdV-mKdV equation based on the multi- symplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from thegeneral solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent 1:o the Preissmann scheme. From the results of the numerical experiments, we can con- clude that the multi-symplectic schemes can accurately sim- ulate the periodic wave solutions of the generalized (2+1)- dimensional KdV-mKdV equation while preserve approxi- mately the conservation laws. 展开更多
关键词 generalized (2 1)-dimensional KdV-mKdVequation Multi-symplectic Periodic wave solution Con-servation law ~ Jacobi elliptic function
下载PDF
New Multiple Soliton-like and Periodic Solutions for (2+l)-Dimensional Canonical Generalized KP Equation with Variable Coefficients 被引量:3
14
作者 ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5X期793-798,共6页
In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit ... In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional OGKP equation with variable coetffcients. 展开更多
关键词 (2+1)-dimensional canonical generalized (CGKP) equation with variable coefficients tanh function method Riccati equation soliton-like and periodic solutions
下载PDF
A Generalized Variable-Coefficient Algebraic Method Exactly Solving (3+1)-Dimensional Kadomtsev-Petviashvilli Equation 被引量:3
15
作者 BAI Cheng-Lin BAI Cheng-Jie ZHAO Hong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第5X期821-826,共6页
A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, th... A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions. 展开更多
关键词 generalized variable-coefficient algebraic method (3+1)-dimensional KP equation exact explicit solutions
下载PDF
Interactions among special embed-solitons for the (3+1)-dimensional Burgers equation 被引量:1
16
作者 张雯婷 戴朝卿 陈未路 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第4期196-199,共4页
With the help of a modified mapping method and a new mapping method, we re-study the (3+1)-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions ... With the help of a modified mapping method and a new mapping method, we re-study the (3+1)-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction. 展开更多
关键词 (3+1)-dimensional burgers equation modified mapping method interaction between special embed-solitons
下载PDF
Lump and interaction solutions to the (3+1)-dimensional Burgers equation
17
作者 Jian Liu Jian-Wen Wu 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第3期50-54,共5页
The(3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics,is considered. Two types of semi-rational solutions, namely, the lump–kink solution and the lump–two ki... The(3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics,is considered. Two types of semi-rational solutions, namely, the lump–kink solution and the lump–two kinks solution, are constructed from the quadratic function ansatz. Some interesting features of interactions between lumps and other solitons are revealed analytically and shown graphically, such as fusion and fission processes. 展开更多
关键词 (3+1)-dimensional burgers equation lump SOLUTION INTERACTION wave SOLUTION BILINEAR form
下载PDF
Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new(3+1)-dimensional generalized Kadomtsev–Petviashvili equation
18
作者 Jian-Wen Wu Yue-Jin Cai Ji Lin 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第3期140-145,共6页
With the aid of the Painlevé analysis, we obtain residual symmetries for a new(3+1)-dimensional generalized Kadomtsev–Petviashvili(gKP) equation. The residual symmetry is localized and the finite transformation ... With the aid of the Painlevé analysis, we obtain residual symmetries for a new(3+1)-dimensional generalized Kadomtsev–Petviashvili(gKP) equation. The residual symmetry is localized and the finite transformation is proposed by introducing suitable auxiliary variables. In addition, the interaction solutions of the(3+1)-dimensional gKP equation are constructed via the consistent Riccati expansion method. Particularly, some analytical soliton-cnoidal interaction solutions are discussed in graphical way. 展开更多
关键词 residual symmetry interaction solutions (3+1)-dimensional generalized Kadomtsev–Petviashvili equation
下载PDF
The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution
19
作者 Xiang-Wen Cheng Zong-Guo Zhang Hong-Wei Yang 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第12期329-339,共11页
The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the ... The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the piecewise function perturbation form is new with great difference from the previous perturbation.Then,based on the piecewise function perturbation,a(3+1)-dimensional generalized modified Korteweg–de Vries Zakharov–Kuznetsov(mKdV-ZK)equation is derived for the first time,which is an extended form of the classical mKdV equation and the ZK equation.The(3+1)-dimensional generalized time-space fractional mKdV-ZK equation is constructed using the semi-inverse method and the fractional variational principle.Obviously,it is more accurate to depict some complex plasma processes and phenomena.Further,the conservation laws of the generalized time-space fractional mKdV-ZK equation are discussed.Finally,using the multi-exponential function method,the non-resonant multiwave solutions are constructed,and the characteristics of ion-acoustic waves are well described. 展开更多
关键词 ion-acoustic waves piecewise function perturbation (3+1)-dimensional generalized time-space fractional mKdV-ZK equation non-resonant multiwave solution
下载PDF
New Compacton-Like and Solitary Pattern-Like Solutions of (2+1)-Dimensional Generalization of Modified KdV Equation
20
作者 CHEN Yong YAN Zhen-Ya 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第5X期789-792,共4页
Recently some (1+1)-dimensional nonlinear wave equations with linearly dispersive terms were shown to possess compacton-like and solitary pattern-like solutions. In this paper, with the aid of Maple, new solutions of ... Recently some (1+1)-dimensional nonlinear wave equations with linearly dispersive terms were shown to possess compacton-like and solitary pattern-like solutions. In this paper, with the aid of Maple, new solutions of (2+1)-dimensional generalization of mKd V equation, which is of only linearly dispersive terms, are investigated using three new transformations. As a consequence, it is shown that this (2+ 1)-dimensional equation also possesses new compacton-like solutions and solitary pattern-like solutions. 展开更多
关键词 (2+1)-dimensional nonlinear wave equation comptacton-like solution solitary pattern-like solution
下载PDF
上一页 1 2 12 下一页 到第
使用帮助 返回顶部