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Second order nonlinear differential equations equivalent to linear differential equations
Kocic, V.Lj., Keckic, J.D.
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Nonlinear differential−difference equations
Journal of Mathematical Physics, 1975A 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, 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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Differential Equations with Bistable Nonlinearity
Ukrainian Mathematical Journal, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Samoilenko, A. M., Nizhnik, I. L.
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Nonlinear Differential Equations
2014We 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, 2016Summary: 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
1997Traditionally 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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