This paper is based on the Darboux transformation of the Kundu-Nonlinear Schrödinger equation. The rogue wave solutions are obtained from periodic seed solutions. After that, the higher order rogue wave soluti...This paper is based on the Darboux transformation of the Kundu-Nonlinear Schrödinger equation. The rogue wave solutions are obtained from periodic seed solutions. After that, the higher order rogue wave solutions of the Kundu-Nonlinear Schrödinger equation are given. Finally, we show that free parameters in eigenfunctions can adjust the patterns of the higher order rogue waves.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
The determinant representation of three-fold Darboux transformation for a variable-coefficient modified KdV equation is displayed based on the technique used to solve Ablowitz-Kaup-Newell-Segur system. Additionally, t...The determinant representation of three-fold Darboux transformation for a variable-coefficient modified KdV equation is displayed based on the technique used to solve Ablowitz-Kaup-Newell-Segur system. Additionally, the nonsingular positon solutions of the variable-coefficient modified KdV equation are firstly discovered analytically and graphically.展开更多
In this paper, we give the Lax pair and construct the Darboux transformation of the Kundu-DNLS equation. Furthermore, the rogue wave solutions of the Kundu-DNLS equation are derived by using the Taylor expansion of th...In this paper, we give the Lax pair and construct the Darboux transformation of the Kundu-DNLS equation. Furthermore, the rogue wave solutions of the Kundu-DNLS equation are derived by using the Taylor expansion of the breather solution. What's more, the triangular and the circular patterns of the third rouge solution are displayed.展开更多
In this paper,we construct Hamiltonian systems for 2 N particles whose force depends on the distances between the particles.We obtain the generalized finite nonperiodic Toda equations via a symmetric group transformat...In this paper,we construct Hamiltonian systems for 2 N particles whose force depends on the distances between the particles.We obtain the generalized finite nonperiodic Toda equations via a symmetric group transformation.The solutions of the generalized Toda equations are derived using the tau functions.The relationship between the generalized nonperiodic Toda lattices and Lie algebras is then be discussed and the generalized Kac-van Moerbeke hierarchy is split into generalized Toda lattices,whose integrability and Darboux transformation are studied.展开更多
Based on the symmetry of the Q-deformed Kadomtsev-Petviashvili(q-KP)hierarchy,which is a q-deformation of the KP hierarchy,we construct the quantum torus symmetry of the q-KP hierarchy,which further leads to the quant...Based on the symmetry of the Q-deformed Kadomtsev-Petviashvili(q-KP)hierarchy,which is a q-deformation of the KP hierarchy,we construct the quantum torus symmetry of the q-KP hierarchy,which further leads to the quantum torus constraint of its tau function.Moreover,we generalize the system to a multi-component q-KP hierarchy that also has the well-known ghost symmetry.展开更多
The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy(BTH).As a specific example of exponential solutions of the BTH,the authors consider a regular solution for the(1,2)-BTH with a 3...The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy(BTH).As a specific example of exponential solutions of the BTH,the authors consider a regular solution for the(1,2)-BTH with a 3×3-sized Lax matrix,and discuss some geometric structures of the solution from which the difference between the(1,2)-BTH and the original Toda hierarchy is shown.After this,the authors construct another kind of Lax representation of(N,1)-BTH which does not use the fractional operator of Lax operator.Then the authors introduce the lattice Miura transformation of(AT,1)-BTH which leads to equations depending on one field,and meanwhile some specific examples which contain the Volterra lattice equation(a useful ecological competition model)are given.展开更多
In this paper, the authors define the noncommutative constrained KadomtsevPetviashvili(KP) hierarchy and multi-component noncommutative constrained KP hierarchy. Then they give the recursion operators for the noncommu...In this paper, the authors define the noncommutative constrained KadomtsevPetviashvili(KP) hierarchy and multi-component noncommutative constrained KP hierarchy. Then they give the recursion operators for the noncommutative constrained KP(NcKP) hierarchy and multi-component noncommutative constrained KP(NmcKP) hierarchy. The authors hope these studies might be useful in the study of D-brane dynamics whose noncommutative coordinates emerge from limits of the M theory and string theory.展开更多
In this paper,the author constructs ghost symmetries of the extended Toda hierarchy with their spectral representations.After this,two kinds of Darboux transforma-tions in different directions and their mixed Darboux ...In this paper,the author constructs ghost symmetries of the extended Toda hierarchy with their spectral representations.After this,two kinds of Darboux transforma-tions in different directions and their mixed Darboux transformations of this hierarchy are constructed.These symmetries and Darboux transformations might be useful in Gromov-Witten theory of CP1.展开更多
基金supported by the NSF of China under Grant No.10971109 and No.11271210 and K.C.Wong Magna Fund in Ningbo Universitysupported by Natural Science Foundation of Ningbo under Grant No.2011A610179.
文摘This paper is based on the Darboux transformation of the Kundu-Nonlinear Schrödinger equation. The rogue wave solutions are obtained from periodic seed solutions. After that, the higher order rogue wave solutions of the Kundu-Nonlinear Schrödinger equation are given. Finally, we show that free parameters in eigenfunctions can adjust the patterns of the higher order rogue waves.
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.
文摘The determinant representation of three-fold Darboux transformation for a variable-coefficient modified KdV equation is displayed based on the technique used to solve Ablowitz-Kaup-Newell-Segur system. Additionally, the nonsingular positon solutions of the variable-coefficient modified KdV equation are firstly discovered analytically and graphically.
文摘In this paper, we give the Lax pair and construct the Darboux transformation of the Kundu-DNLS equation. Furthermore, the rogue wave solutions of the Kundu-DNLS equation are derived by using the Taylor expansion of the breather solution. What's more, the triangular and the circular patterns of the third rouge solution are displayed.
基金the National Natural Science Foundation of China under Grant No.12071237the K C Wong Magna Fund in Ningbo University。
文摘In this paper,we construct Hamiltonian systems for 2 N particles whose force depends on the distances between the particles.We obtain the generalized finite nonperiodic Toda equations via a symmetric group transformation.The solutions of the generalized Toda equations are derived using the tau functions.The relationship between the generalized nonperiodic Toda lattices and Lie algebras is then be discussed and the generalized Kac-van Moerbeke hierarchy is split into generalized Toda lattices,whose integrability and Darboux transformation are studied.
基金supported by the National Natural Science Foundation of China under the grant No.11571192K.C.Wong Magna Fund in Ningbo University.
文摘Based on the symmetry of the Q-deformed Kadomtsev-Petviashvili(q-KP)hierarchy,which is a q-deformation of the KP hierarchy,we construct the quantum torus symmetry of the q-KP hierarchy,which further leads to the quantum torus constraint of its tau function.Moreover,we generalize the system to a multi-component q-KP hierarchy that also has the well-known ghost symmetry.
基金supported by the National Natural Science Foundation of China(Nos.11201251,10971109)the Natural Science Foundation of Zhejiang Province(No.LY12A01007)the K.C.Wong Magna Fundin Ningbo University
文摘The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy(BTH).As a specific example of exponential solutions of the BTH,the authors consider a regular solution for the(1,2)-BTH with a 3×3-sized Lax matrix,and discuss some geometric structures of the solution from which the difference between the(1,2)-BTH and the original Toda hierarchy is shown.After this,the authors construct another kind of Lax representation of(N,1)-BTH which does not use the fractional operator of Lax operator.Then the authors introduce the lattice Miura transformation of(AT,1)-BTH which leads to equations depending on one field,and meanwhile some specific examples which contain the Volterra lattice equation(a useful ecological competition model)are given.
基金supported by the National Natural Science Foundation of China(No.11571192)the Natural Science Foundation of Ningbo(No.2015A610157)K.C.Wong Magna Fund in Ningbo University
文摘In this paper, the authors define the noncommutative constrained KadomtsevPetviashvili(KP) hierarchy and multi-component noncommutative constrained KP hierarchy. Then they give the recursion operators for the noncommutative constrained KP(NcKP) hierarchy and multi-component noncommutative constrained KP(NmcKP) hierarchy. The authors hope these studies might be useful in the study of D-brane dynamics whose noncommutative coordinates emerge from limits of the M theory and string theory.
基金supported by the National Natural Science Foundation of China(No.11571192)K.C.Wong Magna Fund in Ningbo University.
文摘In this paper,the author constructs ghost symmetries of the extended Toda hierarchy with their spectral representations.After this,two kinds of Darboux transforma-tions in different directions and their mixed Darboux transformations of this hierarchy are constructed.These symmetries and Darboux transformations might be useful in Gromov-Witten theory of CP1.