Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled ...Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled system.At last,a Gram-type Pfaffian solution to the new coupled system is given.展开更多
Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial d...Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed.展开更多
In this paper, we obtain the linear differential conditions of （3 ＋ 1）-dimensional Jimbo-Miwa equation and Boiti-Leon-Manna-Pempinelli equation, which guarantee that the corresponding Wronskian determinant solves t...In this paper, we obtain the linear differential conditions of （3 ＋ 1）-dimensional Jimbo-Miwa equation and Boiti-Leon-Manna-Pempinelli equation, which guarantee that the corresponding Wronskian determinant solves the two equations in the Hirota bilinear form. By using the properties of Young diagram, we have proved the results.展开更多
For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct ...For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative version.Meanwhile,we establish the relationship between new and old solutions of the NCLFV hierarchy.Finally,the quasi determinant solutions of the NCLFV hierarchy are obtained.展开更多
In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the m KP equation. It is also shown that the solution of the modified differential-difference ...In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the m KP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a B?cklund transformation for the differentialdifference KP equation with self-consistent sources.展开更多
The paper is the first part of the study of turbulence by using probability dentity functions in which the concept of the grossly determined selutions to the Lundgren’s model equation is introduced, and the equations...The paper is the first part of the study of turbulence by using probability dentity functions in which the concept of the grossly determined selutions to the Lundgren’s model equation is introduced, and the equations for the grossly determiners are derived.展开更多
文摘Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled system.At last,a Gram-type Pfaffian solution to the new coupled system is given.
基金Supported by the National Natural Science Foundation of China under Grant No.11171312
文摘Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed.
基金the National Natural Science Foundation of China(Grant Nos.5110903151379033+7 种基金50921001J110311011201048)Programs Foundation of Ministry of Education of China(Grant No.20100041120037)the Fundamental Research Funds for the Central Universities(Grant Nos.DUT12LK34DUT12LK52)the StateKey Development Program for Basic Research of China(Grant Nos.2013CB0361012010CB32700)
文摘In this paper, we obtain the linear differential conditions of （3 ＋ 1）-dimensional Jimbo-Miwa equation and Boiti-Leon-Manna-Pempinelli equation, which guarantee that the corresponding Wronskian determinant solves the two equations in the Hirota bilinear form. By using the properties of Young diagram, we have proved the results.
基金supported by the National Natural Science Foundation of China under Grant No.12071237KC Wong Magna Fund in Ningbo University。
文摘For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative version.Meanwhile,we establish the relationship between new and old solutions of the NCLFV hierarchy.Finally,the quasi determinant solutions of the NCLFV hierarchy are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11601247 and 11605096the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant Nos.2016MS0115 and 2015MS0116the Innovation Fund Programme of Inner Mongolia University No.201611155
文摘In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the m KP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a B?cklund transformation for the differentialdifference KP equation with self-consistent sources.
文摘The paper is the first part of the study of turbulence by using probability dentity functions in which the concept of the grossly determined selutions to the Lundgren’s model equation is introduced, and the equations for the grossly determiners are derived.
