To describe two correlated events,the Alice-Bob(AB)systems were constructed by Lou through the symmetry of the shifted parity,time reversal and charge conjugation.In this paper,the coupled AB system of the Kadomtsev-P...To describe two correlated events,the Alice-Bob(AB)systems were constructed by Lou through the symmetry of the shifted parity,time reversal and charge conjugation.In this paper,the coupled AB system of the Kadomtsev-Petviashvili equation,which is a useful model in natural science,is established.By introducing an extended Backlund transformation and its bilinear formation,the symmetry breaking soliton,lump and breather solutions of this system are derived with the aid of some ansatze functions.Figures show these fascinating symmetry breaking structures of the explicit solutions.展开更多
Dynamical analysis has revealed that, for some nonlinear wave equations, loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loopsoliton solution consists of three solutions, and is ...Dynamical analysis has revealed that, for some nonlinear wave equations, loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loopsoliton solution consists of three solutions, and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a ＂real＂ loopsolution exists, and if so, what are the precise parametric representations of these loop traveling wave solutions.展开更多
An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves t...An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves the study of a model problem. An analytical and numerical study of this model problem of a thermo-elastic half space containing a surface breaking crack and subjected to oscillatory thermal loading is presented. The crack surface is traction free. In particular, the amplitude of the stress intensity factor at the crack vertex is found as a function of the crack depth and the frequency of thermal oscillation.展开更多
A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equati...A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.展开更多
By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many bre...By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many breaking wave solutions, smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of travelling wave solutions are listed.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11705077,11775104 and 11447017)the Natural Science Foundation of Zhejiang Province(No.LY14A010005)。
文摘To describe two correlated events,the Alice-Bob(AB)systems were constructed by Lou through the symmetry of the shifted parity,time reversal and charge conjugation.In this paper,the coupled AB system of the Kadomtsev-Petviashvili equation,which is a useful model in natural science,is established.By introducing an extended Backlund transformation and its bilinear formation,the symmetry breaking soliton,lump and breather solutions of this system are derived with the aid of some ansatze functions.Figures show these fascinating symmetry breaking structures of the explicit solutions.
基金supported by the National Natural Science Foundation of China (Nos.10671179 and 10831003)
文摘Dynamical analysis has revealed that, for some nonlinear wave equations, loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loopsoliton solution consists of three solutions, and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a ＂real＂ loopsolution exists, and if so, what are the precise parametric representations of these loop traveling wave solutions.
文摘An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves the study of a model problem. An analytical and numerical study of this model problem of a thermo-elastic half space containing a surface breaking crack and subjected to oscillatory thermal loading is presented. The crack surface is traction free. In particular, the amplitude of the stress intensity factor at the crack vertex is found as a function of the crack depth and the frequency of thermal oscillation.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province of China
文摘A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.
基金the National Natural Science Foundation of China (10671179) and (10772158)
文摘By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many breaking wave solutions, smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of travelling wave solutions are listed.
