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Articles 1 - 21 of 21
Full-Text Articles in Non-linear Dynamics
Multiple Soliton Solutions Of (2+1)-Dimensional Potential Kadomtsev-Petviashvili Equation, Mohammad Najafi M.Najafi, Ali Jamshidi
Multiple Soliton Solutions Of (2+1)-Dimensional Potential Kadomtsev-Petviashvili Equation, Mohammad Najafi M.Najafi, Ali Jamshidi
mohammad najafi
We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.
On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions, Vladimir S. Gerdjikov, Rossen Ivanov, Assen V. Kyuldjiev
On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions, Vladimir S. Gerdjikov, Rossen Ivanov, Assen V. Kyuldjiev
Articles
Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann–Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic N-wave equations but mainly the 3- and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave equations with Z2xZ2 reduction group allow breather-like solitons. Finally it is demonstrated that …
Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, Joachim Escher, Rossen Ivanov, Boris Kolev
Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, Joachim Escher, Rossen Ivanov, Boris Kolev
Articles
The geodesic equations of a class of right invariant metrics on the semi-direct product of two Diff(S) groups are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra are found.
Some New Exact Solutions Of The (3+1)-Dimensional Breaking Soliton Equation By The Exp-Function Method, Mohammad Najafi M.Najafi, Mohammad Taghi Darvishi, Maliheh Najafi
Some New Exact Solutions Of The (3+1)-Dimensional Breaking Soliton Equation By The Exp-Function Method, Mohammad Najafi M.Najafi, Mohammad Taghi Darvishi, Maliheh Najafi
mohammad najafi
This paper applies the Exp-function method to search for new exact traveling wave solutions of the (3+1)-dimensional breaking soliton equation, their physical expantions are given graphically.
Smooth And Peaked Solitons Of The Camassa-Holm Equation And Applications, Darryl Holm, Rossen Ivanov
Smooth And Peaked Solitons Of The Camassa-Holm Equation And Applications, Darryl Holm, Rossen Ivanov
Articles
The relations between smooth and peaked soliton solutions are reviewed for the Camassa- Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann- Hilbert problem. The momentum map from the action-angle scattering variables T∗(TN) to the flow momentum (X∗) provides the Eulerian representation of the N-soliton solution of CH in terms of the scattering data and squared eigenfunctions of its isospectral eigenvalue problem. The …
Applications Of Local Fractional Calculus To Engineering In Fractal Time-Space: Local Fractional Differential Equations With Local Fractional Derivative, Yang Xiao-Jun
Xiao-Jun Yang
This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.
A Short Introduction To Local Fractional Complex Analysis, Yang Xiao-Jun
A Short Introduction To Local Fractional Complex Analysis, Yang Xiao-Jun
Xiao-Jun Yang
This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent’s series of complex functions in complex fractal space, and generalized residue theorems are investigated.
Fractional Trigonometric Functions In Complex-Valued Space: Applications Of Complex Number To Local Fractional Calculus Of Complex Function, Yang Xiao-Jun
Xiao-Jun Yang
This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.
A New Viewpoint To The Discrete Approximation: Discrete Yang-Fourier Transforms Of Discrete-Time Fractal Signal, Yang Xiao-Jun
A New Viewpoint To The Discrete Approximation: Discrete Yang-Fourier Transforms Of Discrete-Time Fractal Signal, Yang Xiao-Jun
Xiao-Jun Yang
It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.
Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers
Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers
HMC Senior Theses
The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and …
A Modification Of Extended Homoclinic Test Approach To Solve The (3+1)-Dimensional Potential-Ytsf Equation, Mohammad Najafi, Mohammad Taghi Darvishi
A Modification Of Extended Homoclinic Test Approach To Solve The (3+1)-Dimensional Potential-Ytsf Equation, Mohammad Najafi, Mohammad Taghi Darvishi
mohammad najafi
By means of the extended homoclinic test approach (EHTA) one can solve some nonlinear partial differential equations (NLPDEs) in their bilinear forms. When an NLPDE has no bilinear closed form we can not use this method. We modify the idea of EHTA to obtain some analytic solutions for the (3+1)-dimensional potential-Yu- Toda-Sasa-Fukuyama (YTSF) equation by obtaining a bilinear closed form for it. By comparison of this method and other analytic methods, like HAM, HTA and three-wave methods, we can see that the new idea is very easy and straightforward
Local Fractional Functional Analysis And Its Applications, Yang Xiao-Jun
Local Fractional Functional Analysis And Its Applications, Yang Xiao-Jun
Xiao-Jun Yang
Local fractional functional analysis is a totally new area of mathematics, and a totally new mathematical world view as well. In this book, a new approach to functional analysis on fractal spaces, which can be used to interpret fractal mathematics and fractal engineering, is presented. From Cantor sets to fractional sets, real line number and the spaces of local fractional functions are derived. Local fractional calculus of real and complex variables is systematically elucidated. Some generalized spaces, such as generalized metric spaces, generalized normed linear spaces, generalized Banach's spaces, generalized inner product spaces and generalized Hilbert spaces, are introduced. Elemental …
Local Fractional Laplace’S Transform Based Local Fractional Calculus, Yang Xiaojun
Local Fractional Laplace’S Transform Based Local Fractional Calculus, Yang Xiaojun
Xiao-Jun Yang
In this paper, a new modeling for the local fractional Laplace’s transform based on the local fractional calculus is proposed in fractional space. The properties of the local fractional Laplace’s transform are obtained and an illustrative example for the local fractional system is investigated in detail.
Fundamentals Of Local Fractional Iteration Of The Continuously Nondifferentiable Functions Derived Form Local Fractional Calculus, Yang Xiaojun
Xiao-Jun Yang
A new possible modeling for the local fractional iteration process is proposed in this paper. Based on the local fractional Taylor’s series, the fundamentals of local fractional iteration of the continuously non-differentiable functions are derived from local fractional calculus in fractional space.
Local Fractional Integral Transforms, Yang X
Local Fractional Integral Transforms, Yang X
Xiao-Jun Yang
Over the past ten years, the local fractional calculus revealed to be a useful tool in various areas ranging from fundamental science to various engineering applications, because it can deal with local properties of non-differentiable functions defined on fractional sets. In fractional spaces, a basic theory of number and local fractional continuity of non-differentiable functions are presented, local fractional calculus of real and complex variables is introduced. Some generalized spaces, such as generalized metric spaces, generalized normed linear spaces, generalized Banach’s spaces, generalized inner product spaces and generalized Hilbert spaces, are introduced. Elemental introduction to Yang-Fourier transforms, Yang-Laplace transforms, local …
Termodynamika Procesowa (Dla Me Aparatura Procesowa) Ćw., Wojciech M. Budzianowski
Termodynamika Procesowa (Dla Me Aparatura Procesowa) Ćw., Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
The Analysis Of Heat Transfer In A Gas-Gas Heat Exchanger Operated Under A Heat-Recirculating Mode, Mariusz Salaniec, Wojciech M. Budzianowski
The Analysis Of Heat Transfer In A Gas-Gas Heat Exchanger Operated Under A Heat-Recirculating Mode, Mariusz Salaniec, Wojciech M. Budzianowski
Wojciech Budzianowski
The present paper presents the analysis of heat transfer in a gas-gas heat exchanger operated in a heat-recirculating mode.
An Overview Of Technologies For Upgrading Of Biogas To Biomethane, Wojciech M. Budzianowski
An Overview Of Technologies For Upgrading Of Biogas To Biomethane, Wojciech M. Budzianowski
Wojciech Budzianowski
The present contribution presents an overview of technologies available for upgrading of biogas to biomethane. Technologies under study include pressure swing adsorption (PSA), high-pressure water wash (HPWW), reactive absorption (RA), physical absorption (PA), membrane separation (MS) and cryogenic separation (CS).
Influence Of Energy Policy On The Rate Of Implementation Of Biogas Power Plants In Germany During The 2001-2010 Decade, Izabela Chasiak, Wojciech M. Budzianowski
Influence Of Energy Policy On The Rate Of Implementation Of Biogas Power Plants In Germany During The 2001-2010 Decade, Izabela Chasiak, Wojciech M. Budzianowski
Wojciech Budzianowski
The current article describes energy policy tools, which caused intensive development of biogas-based power generation in Germany during the 2001-2010 decade. The German system of financial support to biogas power plants is presented in details. It is shown that in Germany, i.e. in a country characterised by similar climate and potentials to renewable energy to Poland, biogas power plants cover 10,7% of electricity demands in 2010, while all renewable energy sources cover only 5,4% of electricity demands. It is emphasised that under favourable Polish energy policy, the development of biogas energy can be very rapid.
On The (Non)-Integrability Of Kdv Hierarchy With Self-Consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
On The (Non)-Integrability Of Kdv Hierarchy With Self-Consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
Articles
Nonholonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called “squared solutions” (squared eigenfunctions). Such deformations are equivalent to a perturbed model with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV6 equation are analysed. This allows for a formulation of conditions on the perturbation terms that preserve its integrability. The perturbation corrections to the scattering data and to the corresponding action-angle (canonical) variables are studied. The analysis shows …
Rational Bundles And Recursion Operators For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valtchev
Rational Bundles And Recursion Operators For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valtchev
Articles
We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan’s classification and having additional reductions.