On the decomposition of the modified Kadometsev–Petviashvili equation and the connection between the KN equation and a completely integrable finite-dimensional Hamiltonian system

2004 ◽  
Vol 37 (4) ◽  
pp. 1299-1307 ◽  
Author(s):  
Zhong-Ding Li
Keyword(s):  
Hamiltonian System ◽  
Completely Integrable ◽  
Finite Dimensional ◽  
Petviashvili Equation

THE NONLINEARIZATION OF A (2+1)-DIMENSIONAL SOLITON EQUATION

2008 ◽  
Vol 22 (32) ◽  
pp. 3179-3194
Author(s):  
QIANG LIU ◽  
DIAN-LOU DU
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Hamiltonian System ◽  
Eigenvalue Problem ◽  
Hamiltonian Systems ◽  
Soliton Equation ◽  
Completely Integrable ◽  
Finite Dimensional ◽  
Dimensional Soliton

Based on a 2 × 2 eigenvalue problem, a new (2+1)-dimensional soliton equation is proposed. Moreover, we obtain a finite-dimensional Hamiltonian system. Then we verify it is completely integrable in the Liouville sense. In the end, we introduce a set of Hk polynomial integrable, by which we can separate the solition equation into three compantiable Hamiltonian systems of ordinary differential equation.

Decomposing the Toda hierarchy by an implicit symmetry constraint

2019 ◽  
Vol 33 (03) ◽  
pp. 1950028
Author(s):  
Xi-Xiang Xu ◽  
Min Guo ◽  
Ning Zhang
Keyword(s):  
Hamiltonian System ◽  
Toda Lattice ◽  
Lattice Equation ◽  
Symmetry Constraint ◽  
Completely Integrable ◽  
Toda Hierarchy ◽  
Finite Dimensional ◽  
Symplectic Map ◽  
Toda Lattice Hierarchy

An implicit symmetry constraint of the famous Toda lattice hierarchy is presented. Using this symmetry constraint, every lattice equation in the Toda hierarchy is decomposed by an integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system.

Two integrable extensions of the Kadomtsev-Petviashvili equation

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Kp Equation ◽  
Completely Integrable ◽  
Multiple Soliton Solutions ◽  
Petviashvili Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

AbstractIn this work, two new completely integrable extensions of the Kadomtsev-Petviashvili (eKP) equation are developed. Multiple soliton solutions and multiple singular soliton solutions are derived to demonstrate the compatibility of the extensions of the KP equation.

scholarly journals BINARY NONLINEARIZATION OF THE SUPER AKNS SYSTEM

2008 ◽  
Vol 22 (04) ◽  
pp. 275-288 ◽  
Author(s):  
JINGSONG HE ◽  
JING YU ◽  
YI CHENG ◽  
RUGUANG ZHOU
Keyword(s):  
Hamiltonian System ◽  
Spectral Problem ◽  
Integrable Hamiltonian System ◽  
Integrals Of Motion ◽  
Finite Dimensional ◽  
Akns System ◽  
Hamiltonian Forms

We establish the binary nonlinearization approach of the spectral problem of the super AKNS system, and then use it to obtain the super finite-dimensional integrable Hamiltonian system in the supersymmetry manifold ℝ4N|2N. The super Hamiltonian forms and integrals of motion are given explicitly.

scholarly journals Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jing Yu ◽  
Jingwei Han
Keyword(s):  
Hamiltonian System ◽  
Lie Superalgebra ◽  
Lax Representation ◽  
Lax Pairs ◽  
Finite Dimensional ◽  
Two Component ◽  
Akns System

Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation andr-matrix are also given in this paper.

Stationary Response of Multidegree-of-Freedom Strongly Nonlinear Systems to Fractional Gaussian Noise

2017 ◽  
Vol 84 (10) ◽  
Author(s):  
Qiang Feng Lü ◽  
Mao Lin Deng ◽  
Wei Qiu Zhu
Keyword(s):  
Hamiltonian System ◽  
Gaussian Noise ◽  
Hurst Index ◽  
Fractional Gaussian Noise ◽  
Stationary Response ◽  
Completely Integrable ◽  
Strongly Nonlinear ◽  
Fractional Stochastic Differential Equations ◽  
Strongly Nonlinear System ◽  
Probability Densities

The stationary response of multidegree-of-freedom (MDOF) strongly nonlinear system to fractional Gaussian noise (FGN) with Hurst index 1/2 < H < 1 is studied. First, the system is modeled as FGN-excited and -dissipated Hamiltonian system. Based on the integrability and resonance of the associated Hamiltonian system, the system is divided into five classes: partially integrable and resonant, partially integrable and nonresonant, completely integrable and resonant, completely integrable and nonresonant, and nonintegrable. Then, the averaged fractional stochastic differential equations (SDEs) for five classes of quasi-Hamiltonian systems with lower dimension and involving only slowly varying processes are derived. Finally, the approximate stationary probability densities and other statistics of two example systems are obtained by numerical simulation of the averaged fractional SDEs to illustrate the application and compared with those from original systems to show the advantages of the proposed procedure.

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