Hamiltonian structure of isospectral deformation equation and semi-classical approximation to factorizedS-matrices

1980 ◽  
Vol 4 (6) ◽  
pp. 485-493 ◽  
Author(s):  
D. V. Chudnovsky ◽  
G. V. Chudnovsky
Keyword(s):  
Hamiltonian Structure ◽  
Isospectral Deformation ◽  
Classical Approximation ◽  
Deformation Equation

scholarly journals Hamiltonian Aspects of Three-Layer Stratified Fluids

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
R. Camassa ◽  
G. Falqui ◽  
G. Ortenzi ◽  
M. Pedroni ◽  
T. T. Vu Ho
Keyword(s):  
Hamiltonian Structure ◽  
Linear Equations ◽  
Hamiltonian Formalism ◽  
Reduction Process ◽  
Ideal Fluids ◽  
Upper Lid ◽  
Stratification Structure ◽  
Special Solutions ◽  
Dispersionless Limit ◽  
Unbounded Fluid

AbstractThe theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

scholarly journals Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1077
Author(s):  
Yarema A. Prykarpatskyy
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Structure ◽  
Necessary Condition ◽  
Type Representation ◽  
Infinite Hierarchy ◽  
Polynomial Coefficients ◽  
Kdv Type Equations ◽  
Special Case

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

Machining Deformation Equation of FWP Based on Rayleigh-Leeds Method

2012 ◽  
Vol 562-564 ◽  
pp. 917-920
Author(s):  
Yao Hua Deng ◽  
Gui Xiong Liu
Keyword(s):  
Energy Conditions ◽  
Test Function ◽  
Bending Deformation ◽  
Flexible Workpiece ◽  
Deformation Equation ◽  
Flexible Part ◽  
Minimum Potential ◽  
Deformation Test ◽  
Function Finding ◽  
The Relationship

This paper discusses the FWP bending deformation processing computing problems. Using Rayleigh-Leeds method to solve the flexible part bending deformation. Designing flexible part bending deformation test function. Finding out the flexible part itself material characteristics, the relationship between Fz and deformation through satisfying FWP processing process of a flexible minimum potential energy conditions to work out the approximate solution of the flexible part bending deformation. Finally, think a rectangular flexible workpiece that made of polyurethane sponge as an experiment subject. The results show that the calculated results of the average of the relative deviation are only 6.85%. Proof that this bending deformation test functions satisfies the actual deformation calculation requirements.

scholarly journals REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KdV HIERARCHIES AND THE TWO-MATRIX MODEL

1995 ◽  
Vol 10 (17) ◽  
pp. 2537-2577 ◽  
Author(s):  
H. ARATYN ◽  
E. NISSIMOV ◽  
S. PACHEVA ◽  
A.H. ZIMERMAN
Keyword(s):  
Poisson Bracket ◽  
Hamiltonian Structure ◽  
Toda Lattice ◽  
Free Field ◽  
String Model ◽  
Matrix Formulation ◽  
Hamiltonian Action ◽  
Kdv Hierarchy ◽  
Associated Matrix ◽  
Toda Lattice Hierarchy

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL (M+1, M−k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL (M+1, M−k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M−k) Poisson bracket algebras generalizing the familiar nonlinear WM+1 algebra. Discrete Bäcklund transformations for SL (M+1, M−k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL (M+1, 1) KdV hierarchy.

Hamiltonian structure for a modified discrete self-trapping dimer

1994 ◽  
Vol 4 (2) ◽  
pp. 217-225 ◽  
Author(s):  
Michael J. Jørgensen ◽  
Peter L. Christiansen
Keyword(s):  
Hamiltonian Structure ◽  
Self Trapping
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