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Fuzzy neighborhood-based differential evolution with orientation for nonlinear equation systems
Knowledge-Based Systems, 2019Solving nonlinear equation systems (NESs) plays a vital role in science and engineering. Systems of nonlinear equations typically have more than root. Most of the classical methods cannot locate multiple roots in a single run.
Wei He +4 more
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Nonlinear Differential Equations Equivalent to Solvable Nonlinear Equations
SIAM Journal on Mathematical Analysis, 1976This paper shows in a simple and direct way the equivalence of the nonlinear differential equation $y'' + r(x)y' + q(x)Z(y) = A(y)y'^2 + g(x)z(y)[u(y)]^a $, $Z(y) = z(y)u(y)$, to the linear equation $L_1 u = g(x)$, $a = 0$, or to the nonlinear equation $L_1 u = g(x)u^a $, $a \ne 0$, where $L_1 = {{d^2 } / {dx^2 }} + r(x){d / {dx}} + q(x)$.
Klamkin, Murray S., Reid, James L.
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Neurocomputing, 2015
A recurrent neural dynamics (termed improved Zhang dynamics, IZD), together with a specially-constructed activation function, is proposed and investigated for finding the root of nonlinear equation in this paper.
Lin Xiao, Rongbo Lu
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A recurrent neural dynamics (termed improved Zhang dynamics, IZD), together with a specially-constructed activation function, is proposed and investigated for finding the root of nonlinear equation in this paper.
Lin Xiao, Rongbo Lu
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Solving Nonlinear Equation Systems by a Two-Phase Evolutionary Algorithm
IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021Weifeng Gao +4 more
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Nonlocal Nonlinear Schrödinger Equations
2023The authors treat here the Cauchy problem for Schrödinger equation \[ iu_ t=Au+kg[(Bu,u)]Cu,\quad u(0)=u_ 0.\leqno (1) \] Here \(u\) is a mapping of time interval \(S=[0,T)\) into a complex Hilbert space \(H\) with scalar product \((.,.),\) and \(A,B,C\) denote self-adjoint linear operators on \(H\) with densely defined domain in \(H\). Furthermore \(g\
Heimsoeth, B., Lange, H.
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Nondegenerate soliton dynamics of nonlocal nonlinear Schrödinger equation
Nonlinear dynamics, 2023Kai-Li Geng +4 more
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Abundant optical solitons to the Sasa-Satsuma higher-order nonlinear Schrödinger equation
Optical and quantum electronics, 2021F. S. Khodadad +5 more
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2001
In this chapter we address the problem of approximationg zeros ∝ of nonlinear function f, f (∝ ) = 0, where f ϵ F ⊂ {f : D ⊂ Rd →Rl}. In order to define our solution operators, we first review several error criteria that are commonly used to measure the quality of approximations to zeros of nonlinear equations. This is done for univariate function f :
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In this chapter we address the problem of approximationg zeros ∝ of nonlinear function f, f (∝ ) = 0, where f ϵ F ⊂ {f : D ⊂ Rd →Rl}. In order to define our solution operators, we first review several error criteria that are commonly used to measure the quality of approximations to zeros of nonlinear equations. This is done for univariate function f :
openaire +2 more sources