Integrable discretizations for a generalized sine-Gordon equation and the reductions to the sine-Gordon equation and the short pulse equation [PDF]
arXiv, 2023 In this paper, we propose fully discrete analogues of a generalized sine-Gordon (gsG) equation $u_{t x}=\left(1+\nu \partial_x^2\right) \sin u$. The bilinear equations of the discrete KP hierarchy and the proper definition of discrete hodograph transformations are the keys to the construction.
arxiv
Linear differential equations to solve nonlinear mechanical problems: A novel approach [PDF]
arXiv, 2004 Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations
arxiv
On oscillation of integro-differential equations
TURKISH JOURNAL OF MATHEMATICS, 2018 We study the oscillatory behavior of solutions for integro-differential equations of the form $$x'(t) = e(t) -\int_0^t (t-s)^{\alpha-1}k(t, s)f(s, x(s))\, {\rm ds},\quad t\geq 0,$$ where ...
Agacik Zafer, Said R. Grace
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Solving system of integro differential equations using discrete adomian decomposition method
Journal of Taibah University for Science, 2019 In this paper, we propose a new numerical method for solving system of integro-differential equations featuring Volterra and Fredholm integrals. The proposed method depends on the successful application of the Discrete Adomian Decomposition Method (DADM)
H. O. Bakodah +2 more
doaj +1 more source
Transformation of the linear difference equation into a system of the first order difference equations [PDF]
arXiv, 2018 The transformation of the Nth- order linear difference equation into a system of the first order difference equations is presented. The proposed transformation gives possibility to get new forms of the N-dimensional system of the first order equations that can be useful for analysis of the solutions of the Nth- order difference equations. In particular,
arxiv
Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation [PDF]
, 2017 Three (2+1)-dimensional equations, they are KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the KdV equation have been known already, substituting the solutions of the ...
arxiv +1 more source
Electronic Journal of Differential Equations, 2015 In this work, we generalize so called Green's functional concept in literature to second-order linear integro-differential equation with nonlocal conditions. According to this technique, a linear completely nonhomogeneous nonlocal problem for a second-
Ali Sirma
doaj
On linear and nonlinear integro-differential equations
Journal of Mathematical Analysis and Applications, 1986 AbstractThe decomposition method (Adomian, “Nonlinear Stochastic Operator Equations,” Academic Press, New York, in press; “Stochastic Systems,” Academic Press, New York 1983) is shown to be applicable to integro-differential operator equations.
Randolph Rach, George Adomian
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Analytic-Approximate Solution For An Integro- Differential Equation Arising In Oscillating Magnetic Fields Using Homotopy Analysis Method [PDF]
Iranian Journal of Optimization, 2013 In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered.
H. Saberi-Nik, S. Effati, R. Buzhabadi
doaj
A connection between the shallow-water equations and the Euler-Poincaré equations [PDF]
arXiv, 2014 The Euler-Poincar\'e differential (EPDiff) equations and the shallow water (SW) equations share similar wave characteristics. Using the Hamiltonian structure of the SW equations with flat bottom topography, we establish a connection between the EPDiff equations and the SW equations in one and multi-dimensions.
arxiv