Results 21 to 30 of about 18,904 (165)
Advances in Difference Equations, 2018 This paper aims to obtain an approximate solution for fractional order Riccati differential equations (FRDEs). FRDEs are equivalent to nonlinear Volterra integral equations of the second kind.
Bijan Hasani Lichae +2 more
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Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks
Mathematics, 2022 A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems.
Ilya Boykov +2 more
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Lyapunov Functionals in Integral Equations
Axioms, 2023 Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it is therefore further explored in this paper.
Youssef N. Raffoul, Joseph Raffoul
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Nonlinear Schrödinger equation for integrated photonics
Journal of the Optical Society of America B, 2023 The foundations of nonlinear optics are revisited, and the formalism is applied to waveguide modes. The effects of loss and dispersion are included rigorously along with the vectorial nature of the modes, and a full derivation of a new version of the nonlinear Schrödinger (NLS) equation is presented. This leads to more general expressions for the group
Kevin Bach Gravesen +7 more
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$C^n$-almost periodic and almost periodic solutions for some nonlinear integral equations
Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper, we investigate the existence of $C^n$-almost periodic solution for a class of nonlinear Fredholm integral equations, and the existence of almost periodic solution for a class of nonlinear functional integral equations.
Huisheng Ding +2 more
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2015 We consider the questions of one value solvability of the inverse problem for a nonlinear partial Fredholm type integro-differential equation of the fourth order with degenerate kernel. The method of degenerate kernel is developed for the case of inverse
Tursun K Yuldashev
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A New Integrable Nonlinear Evolution Equation [PDF]
Progress of Theoretical Physics, 1980 Summary: We show that a new integrable nonlinear evolution equation \(iq_ t+(q/\sqrt{1+| q| ^ 2})_ {xx}=0\) is solved exactly by the inverse scattering method. From the Gelfand-Levitan equation, a one-soliton solution is obtained. It is found that a one-soliton solution has two interesting limits, a small amplitude soliton and a bursting soliton.
Shimizu, Toru, Wadati, Miki
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Journal of Function Spaces, 2023 In the present paper, a new efficient technique is described for solving nonlinear mixed partial integrodifferential equations with continuous kernels.
Abeer M. Al-Bugami +2 more
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A Multiple Iterated Integral Inequality and Applications
Journal of Applied Mathematics, 2014 We establish new multiple iterated Volterra-Fredholm type integral inequalities, where the composite function w(u(s)) of the unknown function u with nonlinear function w in integral functions in [Ma, QH, Pečarić, J: Estimates on solutions of some new ...
Zongyi Hou, Wu-Sheng Wang
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Approximate Solutions of Nonlinear Integral Equations Using the Cubic B-Spline Scaling Method
Al-Kitab Journal for Pure SciencesThis paper examines a category of general nonlinear integral equations. These equations also include many special cases, such as functional equations and nonlinear integral equations of the Volterra type.
Mohammed Jabbar Adaay Al-Sharea
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