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Bifurcation analysis and analytical traveling wave solutions of a sasa-satsuma equation involving beta, M-truncated and conformable derivatives using the EGREM method. [PDF]
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A differential-equations algorithm for nonlinear equations
ACM Transactions on Mathematical Software, 1984Summary: DAFNE is a set of FORTRAN subprograms for solving nonlinear equations that implements a method founded on the numerical solution of a Cauchy problem for a system of ordinary differential equations inspired by classical mechanics. This paper gives a detailed description of the method as implemented in DAFNE and reports on the numerical tests ...
Filippo Aluffi-Pentini +2 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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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−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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Software for Nonlinear Partial Differential Equations
ACM Transactions on Mathematical Software, 1975The numerical solution of physically realistic nonlinear partial differential equations (PDEs) is a complicated and highly problem-dependent process which usually requires the scientist to undertake the difficult and time-consuming task of developing his own computer program to solve his problem.
Richard F. Sincovec, Niel K. Madsen
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FOSLL* for Nonlinear Partial Differential Equations
SIAM Journal on Scientific Computing, 2015Summary: In previous work, the first-order system LL* (FOSLL*) method was developed for linear partial differential equations. This approach seeks to minimize the residual of the equations in a dual norm induced by the differential operator, yielding approximations accurate in \(L^2(\Omega)\) rather than \(H^1(\Omega)\) or \(H(\mathrm{Div})\).
Eunjung Lee +2 more
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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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