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Exact Boundary Conditions for the Initial Value Problem of Convex Conservation Laws
exact boundary conditions artificial boundary conditions convex conservation laws Burgers’ (inviscid) equation
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2015/5/4
The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in the-oretical analysis for conservation laws, but also...
Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
Exact solution of $D_N$ type quantum Calogero model mapping to free harmonic oscillators
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2010/12/28
We solve the eigenvalue problem of the DN type of Calogero model by mapping it to a set of decoupled quantum harmonic oscillators through a similarity transformation.In particular, we construct the ei...
Exact solutions for periodic and solitary matter waves in nonlinear lattices
Exact solutions periodic solitary matter waves nonlinear lattices
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2010/12/28
We produce three vast classes of exact periodic and solitonic solutions to the one-dimensional
Gross-Pitaevskii equation (GPE) with the pseudopotential in the form of a nonlinear lattice (NL),induced...
Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions
Symmetry analysis exact solutions semilinear heat flow in multi-dimensions
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2010/11/24
A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve...
Exact solution of a 2D interacting fermion model
Exact solution a 2D interacting fermion model
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2010/11/11
We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model provides an effective description of spinless fermions on a square lattice w...
Lie group classifications and exact solutions for time-fractional Burgers equation
Lie group classifications exact solutions
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2010/11/22
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-f...
Exact Yrast Spectra of Cold Atoms on a Ring
Exact Yrast Spectra of Cold Atoms Ring
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2010/12/16
We propose a methodology to construct excited states with a fixed angular momentum, namely,
“yrast excited states” of finite-size one-dimensional bosonic systems with periodic boundary conditions.
On quasitriangular structures in Hopf algebras arising from exact group factorizations
quasitriangular structures Hopf algebras exact group factorizations
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2010/12/10
We show that bicrossed product Hopf algebras arising from exact factorizations in almost simple finite groups, so in particular, in simple and symmetric groups, admit no uasitriangular structure.
Exact Solutions to the Sine-Gordon Equation
Exact Solutions Sine-Gordon Equation
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2010/4/2
A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable $x$ and the tempor...
More common errors in finding exact solutions of nonlinear differential equations. I
nonlinear differential equations common errors
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2010/4/7
In the recent paper by Kudryashov [Commun. Nonlinear Sci. Numer. Simulat., 2009, V.14, 3507-3529] seven common errors in finding exact solutions of nonlinear differential equations were listed and dis...
THE APPROXIMATIONS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIALBOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS
Oseen equations Artificial boundary Artificial boundary condition Finite element approximation Error estimate
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2007/12/12
We consider the linearized incompressible Navier-Stokes (Oseen)
equations in a flat channel. A sequence of approximations to the exact
boundary condition at an artificial boundary is derived. Then t...
Lax pairs, Painlevé properties and exact solutions of the alogero Korteweg-de Vries equation and a new (2+1)-dimensional equation
Lax pairs Painlevé properties exact solutions the alogero Korteweg-de Vries equation
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2010/11/1
We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2+1)-dimensio...