The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Minru Chen - One of the best experts on this subject based on the ideXlab platform.
-
on w_ 1 infty 3 algebra and Integrable System
Nuclear Physics, 2015Co-Authors: Minru Chen, Shikun Wang, Xiaoli Wang, Weizhong ZhaoAbstract:Abstract We construct the W 1 + ∞ 3-algebra and investigate its connection with the Integrable Systems. Since the W 1 + ∞ 3-algebra with a fixed generator W 0 0 in the operator Nambu 3-bracket recovers the W 1 + ∞ algebra, it is intrinsically related to the KP hierarchy. For the general case of the W 1 + ∞ 3-algebra, we directly derive the KP and KdV equations from the Nambu–Poisson evolution equation with the different Hamiltonian pairs of the KP hierarchy. Due to the Nambu–Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of the W 1 + ∞ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schrodinger equation and give an application in optical soliton.
-
on w_ 1 infty 3 algebra and Integrable System
arXiv: Exactly Solvable and Integrable Systems, 2013Co-Authors: Minru Chen, Shikun Wang, Xiaoli Wang, Weizhong ZhaoAbstract:We construct the $W_{1+\infty}$ 3-algebra and investigate the relation between this infinite-dimensional 3-algebra and the Integrable Systems. Since the $W_{1+\infty}$ 3-algebra with a fixed generator $W^0_0$ in the operator Nambu 3-bracket recovers the $W_{1+\infty}$ algebra, it is natural to derive the KP hierarchy from the Nambu-Poisson evolution equation. For the general case of the $W_{1+\infty}$ 3-algebra, we directly derive the KP and KdV equations from the Nambu-Poisson evolution equation with the different Hamiltonian pairs. We also discuss the connection between the $W_{1+\infty}$ 3-algebra and the dispersionless KdV equations. Due to the Nambu-Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of $W_{1+\infty}$ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schr\"{o}dinger equation and give an application in optical soliton.
-
infinite dimensional 3 algebra and Integrable System
Journal of High Energy Physics, 2012Co-Authors: Minru Chen, Shikun Wang, Weizhong ZhaoAbstract:The relation between the infinite-dimensional 3-algebras and the dispersionless KdV hierarchy is investigated. Based on the infinite-dimensional 3-algebras, we derive two compatible Nambu Hamiltonian structures. Then the dispersionless KdV hierarchy follows from the Nambu-Poisson evolution equation given the suitable Hamiltonians. We find that the dispersionless KdV System is not only a bi-Hamiltonian System, but also a bi-Nambu-Hamiltonian System. Due to the Nambu-Poisson evolution equation involving two Hamiltonians, more intriguing relationships between these Hamiltonians are revealed. As an application, we investigate the System of polytropic gas equations and derive an Integrable gas dynamics System in the framework of Nambu mechanics.
Weizhong Zhao - One of the best experts on this subject based on the ideXlab platform.
-
on w_ 1 infty 3 algebra and Integrable System
Nuclear Physics, 2015Co-Authors: Minru Chen, Shikun Wang, Xiaoli Wang, Weizhong ZhaoAbstract:Abstract We construct the W 1 + ∞ 3-algebra and investigate its connection with the Integrable Systems. Since the W 1 + ∞ 3-algebra with a fixed generator W 0 0 in the operator Nambu 3-bracket recovers the W 1 + ∞ algebra, it is intrinsically related to the KP hierarchy. For the general case of the W 1 + ∞ 3-algebra, we directly derive the KP and KdV equations from the Nambu–Poisson evolution equation with the different Hamiltonian pairs of the KP hierarchy. Due to the Nambu–Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of the W 1 + ∞ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schrodinger equation and give an application in optical soliton.
-
on w_ 1 infty 3 algebra and Integrable System
arXiv: Exactly Solvable and Integrable Systems, 2013Co-Authors: Minru Chen, Shikun Wang, Xiaoli Wang, Weizhong ZhaoAbstract:We construct the $W_{1+\infty}$ 3-algebra and investigate the relation between this infinite-dimensional 3-algebra and the Integrable Systems. Since the $W_{1+\infty}$ 3-algebra with a fixed generator $W^0_0$ in the operator Nambu 3-bracket recovers the $W_{1+\infty}$ algebra, it is natural to derive the KP hierarchy from the Nambu-Poisson evolution equation. For the general case of the $W_{1+\infty}$ 3-algebra, we directly derive the KP and KdV equations from the Nambu-Poisson evolution equation with the different Hamiltonian pairs. We also discuss the connection between the $W_{1+\infty}$ 3-algebra and the dispersionless KdV equations. Due to the Nambu-Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of $W_{1+\infty}$ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schr\"{o}dinger equation and give an application in optical soliton.
-
infinite dimensional 3 algebra and Integrable System
Journal of High Energy Physics, 2012Co-Authors: Minru Chen, Shikun Wang, Weizhong ZhaoAbstract:The relation between the infinite-dimensional 3-algebras and the dispersionless KdV hierarchy is investigated. Based on the infinite-dimensional 3-algebras, we derive two compatible Nambu Hamiltonian structures. Then the dispersionless KdV hierarchy follows from the Nambu-Poisson evolution equation given the suitable Hamiltonians. We find that the dispersionless KdV System is not only a bi-Hamiltonian System, but also a bi-Nambu-Hamiltonian System. Due to the Nambu-Poisson evolution equation involving two Hamiltonians, more intriguing relationships between these Hamiltonians are revealed. As an application, we investigate the System of polytropic gas equations and derive an Integrable gas dynamics System in the framework of Nambu mechanics.
Oleg Chalykh - One of the best experts on this subject based on the ideXlab platform.
-
inozemtsev System as seiberg witten Integrable System
Journal of High Energy Physics, 2021Co-Authors: Philip C Argyres, Oleg ChalykhAbstract:In this work we establish that the Inozemtsev System is the Seiberg-Witten Integrable System encoding the Coulomb branch physics of 4d $$ \mathcal{N} $$ = 2 USp(2N) gauge theory with four fundamental and (for N ≥ 2) one antisymmetric tensor hypermultiplets. We describe the transformation from the spectral curves and canonical one-forms of the Inozemtsev System in the N = 1 and N = 2 cases to the Seiberg-Witten curves and differentials explicitly, along with the explicit matching of the modulus of the elliptic curve of spectral parameters to the gauge coupling of the field theory, and of the couplings of the Inozemtsev System to the field theory mass parameters. This result is a particular instance of a more general correspondence between crystallographic elliptic Calogero-Moser Systems with Seiberg-Witten Integrable Systems, which will be explored in future work.
-
inozemtsev System as seiberg witten Integrable System
arXiv: High Energy Physics - Theory, 2021Co-Authors: Philip C Argyres, Oleg ChalykhAbstract:In this work we establish that the Inozemtsev System is the Seiberg-Witten Integrable System encoding the Coulomb branch physics of 4d $\mathcal{N}=2$ USp(2N) gauge theory with four fundamental and (for $N \geq 2$) one antisymmetric tensor hypermultiplets. We describe the transformation from the spectral curves and canonical one-form of the Inozemtsev System in the $N=1$ and $N=2$ cases to the Seiberg-Witten curves and differentials explicitly, along with the explicit matching of the modulus of the elliptic curve of spectral parameters to the gauge coupling of the field theory, and of the couplings of the Inozemtsev System to the field theory mass parameters. This result is a particular instance of a more general correspondence between crystallographic elliptic Calogero-Moser Systems with Seiberg-Witten Integrable Systems, which will be explored in future work.
Xiaoli Wang - One of the best experts on this subject based on the ideXlab platform.
-
on w_ 1 infty 3 algebra and Integrable System
Nuclear Physics, 2015Co-Authors: Minru Chen, Shikun Wang, Xiaoli Wang, Weizhong ZhaoAbstract:Abstract We construct the W 1 + ∞ 3-algebra and investigate its connection with the Integrable Systems. Since the W 1 + ∞ 3-algebra with a fixed generator W 0 0 in the operator Nambu 3-bracket recovers the W 1 + ∞ algebra, it is intrinsically related to the KP hierarchy. For the general case of the W 1 + ∞ 3-algebra, we directly derive the KP and KdV equations from the Nambu–Poisson evolution equation with the different Hamiltonian pairs of the KP hierarchy. Due to the Nambu–Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of the W 1 + ∞ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schrodinger equation and give an application in optical soliton.
-
on w_ 1 infty 3 algebra and Integrable System
arXiv: Exactly Solvable and Integrable Systems, 2013Co-Authors: Minru Chen, Shikun Wang, Xiaoli Wang, Weizhong ZhaoAbstract:We construct the $W_{1+\infty}$ 3-algebra and investigate the relation between this infinite-dimensional 3-algebra and the Integrable Systems. Since the $W_{1+\infty}$ 3-algebra with a fixed generator $W^0_0$ in the operator Nambu 3-bracket recovers the $W_{1+\infty}$ algebra, it is natural to derive the KP hierarchy from the Nambu-Poisson evolution equation. For the general case of the $W_{1+\infty}$ 3-algebra, we directly derive the KP and KdV equations from the Nambu-Poisson evolution equation with the different Hamiltonian pairs. We also discuss the connection between the $W_{1+\infty}$ 3-algebra and the dispersionless KdV equations. Due to the Nambu-Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of $W_{1+\infty}$ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schr\"{o}dinger equation and give an application in optical soliton.
Zhijun Qiao - One of the best experts on this subject based on the ideXlab platform.
-
an Integrable System with peakon complex peakon weak kink and kink peakon interactional solutions
Communications in Nonlinear Science and Numerical Simulation, 2018Co-Authors: Baoqiang Xia, Zhijun QiaoAbstract:Abstract In this paper, we study an Integrable System with both quadratic and cubic nonlinearity: m t = b u x + 1 2 k 1 [ m ( u 2 − u x 2 ) ] x + 1 2 k 2 ( 2 m u x + m x u ) , m = u − u x x , where b, k1 and k2 are arbitrary constants. This model is kind of a cubic generalization of the Camassa–Holm (CH) equation: m t + m x u + 2 m u x = 0 . The equation is shown Integrable with its Lax pair, bi-Hamiltonian structure, and infinitely many conservation laws. In the case b = 0 , peaked soliton (peakon), complex peakon, and multi-peakon solutions are studied. In particular, the two-peakon dynamical System is explicitly presented and their collisions are investigated in details. In the case b ≠ 0, the weak kink and kink-peakon interactional solutions are found for the first time. Significant difference from the CH equation is analyzed through a comparison. In the paper, we also investigate all possible smooth one-soliton solutions for the System.
-
a new two component Integrable System with peakon solutions
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2015Co-Authors: Baoqiang Xia, Zhijun QiaoAbstract:A new two-component System with cubic nonlinearity and linear dispersion: mt=bux+12[m(uv−uxvx)]x−12m(uvx−uxv),nt=bvx+12[n(uv−uxvx)]x+12n(uvx−uxv),m=u−uxx,n=v−vxx,where b is an arbitrary real consta...
-
a new two component Integrable System with peakon solutions
arXiv: Exactly Solvable and Integrable Systems, 2012Co-Authors: Baoqiang Xia, Zhijun QiaoAbstract:A new two-component System with cubic nonlinearity and linear dispersion: \begin{eqnarray*} \left\{\begin{array}{l} m_t=bu_{x}+\frac{1}{2}[m(uv-u_xv_x)]_x-\frac{1}{2}m(uv_x-u_xv), \\ n_t=bv_{x}+\frac{1}{2}[ n(uv-u_xv_x)]_x+\frac{1}{2} n(uv_x-u_xv), \\m=u-u_{xx},~~ n=v-v_{xx}, \end{array}\right. \end{eqnarray*} where $b$ is an arbitrary real constant, is proposed in this paper. This System is shown Integrable with its Lax pair, bi-Hamiltonian structure, and infinitely many conservation laws. Geometrically, this System describes a nontrivial one-parameter family of pseudo-spherical surfaces. In the case $b=0$, the peaked soliton (peakon) and multi-peakon solutions to this two-component System are derived. In particular, the two-peakon dynamical System is explicitly solved and their interactions are investigated in details. Moreover, a new Integrable cubic nonlinear equation with linear dispersion \begin{eqnarray*} m_t=bu_{x}+\frac{1}{2}[m(|u|^2-|u_x|^2)]_x-\frac{1}{2}m(uu^\ast_x-u_xu^\ast), \quad m=u-u_{xx}, \end{eqnarray*} is obtained by imposing the complex conjugate reduction $v=u^\ast$ to the two-component System. The complex valued $N$-peakon solution and kink wave solution to this complex equation are also derived.
-
Integrable System with peakon weak kink and kink peakon interactional solutions
arXiv: Exactly Solvable and Integrable Systems, 2012Co-Authors: Baoqiang Xia, Zhijun QiaoAbstract:In this paper, we study an Integrable System with both quadratic and cubic nonlinearity: $m_t=bu_x+1/2k_1[m(u^2-u^2_x)]_x+1/2k_2(2m u_x+m_xu)$, $m=u-u_{xx}$, where $b$, $k_1$ and $k_2$ are arbitrary constants. This model is kind of a cubic generalization of the Camassa-Holm (CH) equation: $m_t+m_xu+2mu_x=0$. The equation is shown Integrable with its Lax pair, bi-Hamiltonian structure, and infinitely many conservation laws. In the case of $b=0$, the peaked soliton (peakon) and multi-peakon solutions are studied. In particular, the two-peakon dynamical System is explicitly presented and their collisions are investigated in details. In the case of $b\neq0$ and $k_2=0$, the weak kink and kink-peakon interactional solutions are found. Significant difference from the CH equation is analyzed through a comparison. In the paper, we also study all possible smooth one-soliton solutions for the System.
-
generalized r matrix structure and algebro geometric solution for Integrable System
Reviews in Mathematical Physics, 2001Co-Authors: Zhijun QiaoAbstract:The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional Systems and an approach to obtain the algebro-geometric solutions of Integrable nonlinear evolution equations (NLEEs). Our starting point is a generalized Lax matrix instead of the usual Lax pair. The generalized r-matrix structure and Hamiltonian functions are presented on the basis of fundamental Poisson bracket. It can be clearly seen that various nonlinear constrained (c-) and restricted (r-) Systems, such as the c-AKNS, c-MKdV, c-Toda, r-Toda, c-Levi, etc, are derived from the reductions of this structure. All these nonlinear Systems have r-matrices, and are completely Integrable in Liouville's sense. Furthermore, our generalized structure is developed to become an approach to obtain the algebro-geometric solutions of Integrable NLEEs. Finally, the two typical examples are considered to illustrate this approach: the infinite or periodic Toda lattice equation and the AKNS equation with the condition of decay at infinity or periodic boundary.
