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Solving Linear Differential Equations: A Novel Approach
Linear Differential Equations Novel Approach Mathematical Physics
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2012/5/24
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the...
"Quantization" of higher hamiltonian analogues of the Painleve I and Painleve II equations with two degrees of freedom
Quantization higher hamiltonian analogues Painleve I Painleve II equations Exactly Solvable and Integrable Systems
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2012/4/27
We construct a solution of an analog of the Schr\"{o}dinger equation for the Hamiltonian $ H_I (z, t, q_1, q_2, p_1, p_2) $ corresponding to the second equation $P_1^2$ in the Painleve I hierarchy. Th...
Integrable equations and classical S-matrix
Integrable equations classical S-matrix Mathematical Physics
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2012/4/26
We study amplitudes of five-wave interactions for evolution Hamiltonian equations differ from the KdV equation by the form of dispersion law. We find that five-wave amplitude is canceled for all three...
Iterative Solution of Maxwell's Equations for an Induction Motor
Iterative Solution of Maxwell's Equations Induction Motor General Physics
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2012/4/19
In this work we use classical electromagnetism to analyse a three-phase induction motor. We first cast the motor as a boundary value problem involving two phenomenological time-constants. These are de...
The Jacobi last multiplier for difference equations
Jacobi Last Multiplier first order lineal partial differential difference equations
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2012/2/29
We present a discretization of the Jacobi last multiplier, with some applications to the computation of solutions of difference equations.
Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media
Fractional integro-differentiation fractional damping universal response electromagnetic field dielectric medium
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2011/9/23
Abstract: We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equatio...
Exact polynomial solutions of second order differential equations and their applications
Polynomial solutions Bethe ansatz Quasi-exactly solvable systems
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2011/9/21
Abstract: We find all polynomials $Z(z)$ such that the differential equation $${X(z)\frac{d^2}{dz^2}+Y(z)\frac{d}{dz}+Z(z)}S(z)=0,$$ where $X(z), Y(z), Z(z)$ are polynomials of degree at most 4, 3, 2 ...
Differential-difference equations associated with the fractional Lax operators
Lax pair discretization Bogoyavlensky lattice Sawada Kotera equation Kaup Kupershmidt equation
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2011/9/30
Abstract: We study integrable hierarchies associated with spectral problems of the form $P\psi=\lambda Q\psi$ where $P,Q$ are difference operators. The corresponding nonlinear differential-difference ...
Absence of traveling wave solutions of conductivity type for the Novikov-Veselov equations at zero energy
traveling wave conductivity type the Novikov-Veselov equations zero energy
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2011/7/27
Abstract: We prove that the Novikov-Veselov equation (an analog of KdV in dimension 2 + 1) at zero energy does not have sufficiently localized soliton solutions of conductivity type.
Markov evolutions and hierarchical equations in the continuum: II. Multicomponent systems
Continuous system Markov generator Markov process Stochastic dynamics Configuration spaces Birth-and-death process
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2011/7/26
Abstract: General birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations fo...
Dirac-Kahler equations on curved spacetimes
Dirac-Kahler equation local-Minkowskian spacetimes Lagrangian theory Hodge duality Proca field
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2011/7/28
Abstract: A Lagrangian theory giving rise to a version of the Dirac-Kahler equations on curved backgrounds is considered. The principal pieces are the general fields which have values in the algebra o...
Complete group classification of a class of nonlinear wave equations
Complete group classification nonlinear wave equations Analysis of PDEs
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2011/7/26
Abstract: Preliminary group classification became prominent as an approach to symmetry analysis of differential equations due to the paper by Ibragimov, Torrisi and Valenti [J. Math. Phys. 32, 2988-29...
Applications of local fractional calculus to engineering in fractal time-space: Local fractional differential equations with local fractional derivative
local fractional calculus fractal time-space local fractional derivative local fractional differential equation
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2011/7/26
Abstract: 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 eq...
Convergence of the Neumann series for the Schrodinger equation and general Volterra equations in Banach spaces
Neumann Convergence the Schrodinger equation
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2011/7/26
Abstract: The objective of the article is to treat the Schrodinger equation in parallel with a standard treatment of the heat equation. In the mathematics literature, the heat equation initial value p...
Families of integrable equations
Integrable lattice equations Yang-Baxter maps Consistency around the cube
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2011/7/27
Abstract: We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3-parameters and their members are connected through B\"acklund tran...