scholarly journals On the non-local hydrodynamic-type system and its soliton-like solutions

2012 ◽  
Vol 45 (8) ◽  
pp. 085210 ◽  
Author(s):  
V A Vladimirov ◽  
E V Kutafina ◽  
B Zorychta
Keyword(s):  
Type System ◽  
Hydrodynamic Type ◽  
Hydrodynamic Type System ◽  
Non Local

scholarly journals Classification of bi-Hamiltonian pairs extended by isometries

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210185
Author(s):  
Maxim V. Pavlov ◽  
Pierandrea Vergallo ◽  
Raffaele Vitolo
Keyword(s):  
Type System ◽  
Local Part ◽  
First Order ◽  
Hydrodynamic Type System ◽  
Dependent Variables ◽  
Particular Solution ◽  
Non Local ◽  
Hamiltonian Operators ◽  
Hamiltonian Pair

The aim of this article is to classify pairs of the first-order Hamiltonian operators of Dubrovin–Novikov type such that one of them has a non-local part defined by an isometry of its leading coefficient. An example of such a bi-Hamiltonian pair was recently found for the constant astigmatism equation. We obtain a classification in the case of two dependent variables, and a significant new example with three dependent variables that is an extension of a hydrodynamic-type system obtained from a particular solution of the Witten–Dijkgraaf–Verlinde–Verlinde equations.

EQUILIBRIUM THERMODYNAMICS OF SIMPLE HYDRODYNAMIC TYPE SYSTEM

1987 ◽  
Vol 01 (05n06) ◽  
pp. 221-224
Author(s):  
D.P. SANKOVICH
Keyword(s):  
Correlation Functions ◽  
Type System ◽  
Hydrodynamic Type ◽  
Equilibrium Thermodynamics ◽  
Hamiltonian Density ◽  
One Dimensional ◽  
Hydrodynamic Type System ◽  
The One

A generating thermodynamic functional for the one-dimensional, one-component hydrodynamic type system with the Hamiltonian density au2+bu4is determined. Correlation functions of this model are considered.

scholarly journals A gluing approach for the fractional Yamabe problem with isolated singularities

2020 ◽  
Vol 2020 (763) ◽  
pp. 25-78 ◽  
Author(s):  
Weiwei Ao ◽  
Azahara DelaTorre ◽  
María del Mar González ◽  
Juncheng Wei
Keyword(s):  
Approximate Solution ◽  
Reduction Method ◽  
Type System ◽  
Singular Solutions ◽  
Yamabe Problem ◽  
Local Problem ◽  
Infinite Dimensional ◽  
Isolated Points ◽  
Non Local ◽  
First Time

AbstractWe construct solutions for the fractional Yamabe problem that are singular at a prescribed number of isolated points. This seems to be the first time that a gluing method is successfully applied to a non-local problem in order to construct singular solutions. There are two main steps in the proof: to construct an approximate solution by gluing half bubble towers at each singular point, and then an infinite-dimensional Lyapunov–Schmidt reduction method, that reduces the problem to an (infinite-dimensional) Toda-type system. The main technical part is the estimate of the interactions between different bubbles in the bubble towers.

Algebraic Traveling Wave Solutions of a Non-local Hydrodynamic-type Model

2014 ◽  
Vol 17 (3-4) ◽  
pp. 465-482 ◽  
Author(s):  
Aiyong Chen ◽  
Wenjing Zhu ◽  
Zhijun Qiao ◽  
Wentao Huang
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Hydrodynamic Type ◽  
Type Model ◽  
Wave Solutions ◽  
Non Local
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