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On solutions of Maxwell’s equations with dipole sources over a thin conducting film
solutions of Maxwell’s equations dipole sources conducting film
2015/10/16
We derive and interpret solutions of time-harmonic Maxwell’s equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. Graphene sheet, lying between two unbo...
Construction of dKP and BKP Equations with Self-consistent Sources
Construction dKP BKP Equations Self-consistent Sources
2012/8/7
A new procedure is 痳stly proposed to construct soliton equations
with self-consistent sources(SESCSs) in bilinear forms, starting from the Gram-type
determinant solution or Gram-type pfa盿n solution ...
Solving Linear Differential Equations: A Novel Approach
Linear Differential Equations Novel Approach Mathematical Physics
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
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
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
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
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
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
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
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
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
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
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
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
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...