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Linearisation of a second-order nonlinear ordinary differential equation
Acta Polytechnica, 2023 We analyse nonlinear second-order differential equations in terms of algebraic properties by reducing a nonlinear partial differential equation to a nonlinear second-order ordinary differential equation via the point symmetry f(v)∂v.
Adhir Maharaj +3 more
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Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations
Mathematics, 2023 Differential equations are useful mathematical tools for solving complex problems. Differential equations include ordinary and partial differential equations.
Liang Song, Shaodong Chen, Guoxin Wang
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Axioms, 2023 Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method.
Nikolay K. Vitanov
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Solutions of nonlinear differential equations [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2009 We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the article we formulate necessary and sufficient conditions when the solution of the given equation in algebra of new ...
Bedziuk, Nadzeya, Yablonski, Aleh
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Adapting the range of validity for the Carleman linearization [PDF]
Advances in Radio Science, 2016 In this contribution, the limitations of the Carleman linearization approach are presented and discussed. The Carleman linearization transforms an ordinary nonlinear differential equation into an infinite system of linear differential equations. In order
H. Weber, W. Mathis
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Perturbations of nonlinear differential equations [PDF]
Transactions of the American Mathematical Society, 1973 Scalar and vector comparison techniques are used to study the comparative asymptotic behavior of the systems (I) x' = f(t,x) and (2) y' = f(t,y) + g(t,y). Conditions are given which allow bounds for the solutions of (2) to-be obtained assuming a knowledge of the solutions of (1) and which guarantee the generalized asymptotic equivalence of (1) and (2).
Fennell, R. E., Proctor, T. G.
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Discrete Dynamics in Nature and Society, 2022 The main purpose of the current paper is to study the phase portraits and bounded and singular traveling wave solution of the stochastic nonlinear Biswas–Arshed equation by using the “three-step method” of Professor Li’s method together with the phase ...
Yong Tang, Wei Zeng, Zhao Li
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Mathematics, 2022 In this article, a scalar nonlinear integro-differential equation of second order and a non-linear system of integro-differential equations with infinite delays are considered.
Cemil Tunç, Osman Tunç
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Nonlinear elliptic differential equations with multivalued nonlinearities [PDF]
Proceedings Mathematical Sciences, 2001 In this work, certain quasilinear elliptic boundary value problems are investigated. Homogeneous Dirichlet boundary condition is always considered. In the first result, assuming that the multivalued monotone nonlinearity \(\beta\) satisfies \(\operatorname {dom}\beta = R\) and the existence of an upper and a lower solution, the existence of a solution ...
Fiacca A +3 more
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Journal of Applied Mathematics, 2012 We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable
Khaled A. Gepreel +2 more
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