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Linear superposition of nonlinear waves
"... Abstract. Exact nonlinear (arbitrary amplitude) wavelike solutions of an incompressible, magnetized, nondissipative twofluid system are found. It is shown that, in 1D propagation, these fully nonlinear solutions display a rare property; they can be linearly superposed. The Alfvénic systemslike ..."
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suitable conditions, the LNL waves obey a linear superposition principle, i.e. the sum of two or more fully nonlinear solutions is also a solution. To the best of our knowledge, this property is rarely found in nontrivial physical systems These rare cases, however, are extremely important and interesting
Linear Superposition in Nonlinear Equations
, 2002
"... Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions. This procedure works by virtue of some remarkable new identities satisfied by the ellip ..."
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Cited by 6 (2 self)
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Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions. This procedure works by virtue of some remarkable new identities satisfied
In the case of an instantaneous linear superposition
"... In this paper, we propose a method for the online blind separation of sound sources in the case where the mixing filters have a Æshaped impulse response. Our algorithm works entirely in the frequency domain and exhibits fast convergence due to crossfrequency couplings. Specific problems related t ..."
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In this paper, we propose a method for the online blind separation of sound sources in the case where the mixing filters have a Æshaped impulse response. Our algorithm works entirely in the frequency domain and exhibits fast convergence due to crossfrequency couplings. Specific problems related to online separation of running speech are discussed. The algorithm performs successful separation of digitally mixed speech signals and of signals from a moving and a standing speaker recorded in an anechoic chamber.
Stereo matching with linear superposition of layers
 IEEE Trans. Pattern Anal. Machine Intell
, 2006
"... In this paper, we address stereo matching in the presence of a class of nonLambertian effects, where image formation can be modeled as the additive superposition of layers at different depths. The presence of such effects makes it impossible for traditional stereo vision algorithms to recover depth ..."
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Cited by 19 (3 self)
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In this paper, we address stereo matching in the presence of a class of nonLambertian effects, where image formation can be modeled as the additive superposition of layers at different depths. The presence of such effects makes it impossible for traditional stereo vision algorithms to recover
Periodic solutions of nonlinear equations obtained by linear superposition
 J. Phys. A: Math. Gen
, 2002
"... We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the KadomtsevPetviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sineGordon equation and the Boussinesq ..."
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Cited by 6 (2 self)
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We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the KadomtsevPetviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sineGordon equation and the Boussinesq
On Linear Superposition Principle Applying to Hirota Bilinear Equations
"... Abstract The linear superposition principle of exponential travelling waves is analysed for equations of Hirota bilinear type, with an aim to construct a specific subclass of Nsoliton solutions formed by linear co mb ination of exponential travelling waves. Applications are made for SawadaKotera ..."
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Abstract The linear superposition principle of exponential travelling waves is analysed for equations of Hirota bilinear type, with an aim to construct a specific subclass of Nsoliton solutions formed by linear co mb ination of exponential travelling waves. Applications are made for Sawada
Approximation by Superpositions of a Sigmoidal Function
, 1989
"... In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate fun ..."
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Cited by 1248 (2 self)
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In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate
Peculiarities of Bounds on States through the Concept of Linear Superposition
"... We investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We also investigate the entanglement behaviour of such classes of states, specifically their monotone nature. Finally we are able to construct some counterintuitive situations ..."
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We investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We also investigate the entanglement behaviour of such classes of states, specifically their monotone nature. Finally we are able to construct some counterintuitive
New Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition
, 2002
"... We find new periodic solutions of the KadomtsevPetviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sineGordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure for generating sol ..."
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Cited by 1 (0 self)
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We find new periodic solutions of the KadomtsevPetviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sineGordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure for generating
Results 1  10
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48,062