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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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Nonlocal Nonlinear Schrödinger Equations

2023
The 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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Nonlinear equations

2019
Victor Henner   +2 more
  +6 more sources

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