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Method for finding highly dispersive optical solitons of nonlinear differential equations

Optik, 2020
A method for finding solitary wave solutions to nonlinear differential equations is presented. A generalization for the logistic function to obtain a solitary wave solution is introduced. Properties of this basic function are discussed.
N. Kudryashov
semanticscholar   +3 more sources

Solutions of the linear and nonlinear differential equations within the generalized fractional derivatives.

Chaos, 2019
The main goal of this work is to find the solutions of linear and nonlinear fractional differential equations with the Mittag-Leffler nonsingular kernel. An accurate numerical method to search this problem has been constructed.
E. Akgül
semanticscholar   +3 more sources

Nonlinear Differential Equations

2022
Arnaud Ducrot   +3 more
semanticscholar   +3 more sources

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.
openaire   +1 more source

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.
openaire   +2 more sources

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