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Nonlinear differential−difference equations

Journal of Mathematical Physics, 1975
A method is presented which enables one to obtain and solve certain classes of nonlinear differential−difference equations. The introduction of a new discrete eigenvalue problem allows the exact solution of the self−dual network equations to be found by inverse scattering.
Ablowitz, M. J., Ladik, F.
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Nonlinear Differential Equations Equivalent to Solvable Nonlinear Equations

SIAM Journal on Mathematical Analysis, 1976
This 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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Differential Equations with Bistable Nonlinearity

Ukrainian Mathematical Journal, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Samoilenko, A. M., Nizhnik, I. L.
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Nonlinear Differential Equations

2014
We now turn our attention to the initial-value problem for a nonlinear differential equation of the form $$ \dot{x}\left( t \right) = f\left( {t,x\left( t \right)} \right),\quad x\left( \tau \right) = \xi ,\quad \left( {\tau ,\xi } \right) \in J \times G, $$ where \( J \subset {\mathbb{R}} \) is an interval, G is a non-empty open subset of ...
Hartmut Logemann, Eugene P. Ryan
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Differential Identities for Nonlinear Partial Differential Equations

Journal of Mathematical Sciences, 2016
Summary: We obtain new algebraic analytic presentations for solutions and coefficients of nonlinear second order differential equations and systems of such equations.
Anikonov, Yu. E., Neshchadim, M. V.
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Nonlinear Differential Equations

1997
Traditionally all the macroscopic phenomena observed in nature have been studied via solutions of differential equations which are described by smooth and continuous curves. This approach works very well for a class of problem like the planetary motion where the orbits are regular geometric objects (namely, ellipsi).
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Nonlinear Differential Equations

2022
Arnaud Ducrot   +3 more
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