Results 41 to 50 of about 4,406,486 (167)
On a transformation between hierarchies of integrable equations [PDF]
, 2005 A transforation between a hierarchy of integrable equations arising from the standard $R$-matrix construction on the algebra of differential operators and a hierarchy of integrable equations arising from a deformation of the standard $R$-matrix is given.
arxiv +1 more source
The Two-Term Abel’s Integral Equation
Journal of Mathematical Extension, 2012 In this article we investigate the two-term Abel’s integral equations. We will do this in two different ways and show that such equation is reducible to an integro−differential equation of Volterra type.
F. M. Maalek Ghaini +2 more
doaj
Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation
International Journal of Mathematics and Mathematical Sciences, 1999 The generalized forced Boussinesq equation, utt−uxx+[f(u)]xx+uxxxx=h0, and its periodic traveling wave solutions are considered. Using the transform z=x−ωt, the equation is converted to a nonlinear ordinary differential equation with periodic boundary ...
Kenneth L. Jones, Yunkai Chen
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Constructive method for solvability of Fredholm equation of the first kind
Electronic Journal of Qualitative Theory of Differential Equations, 2017 The solvability and construction of the general solution of the first kind Fredholm integral equation are among the insufficiently explored problems in mathematics. There are various approaches to solve this problem.
Serikbai Aisagaliev, Zhanat Zhunussova
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Fourier form of the dressing method: simple example of integrable (2+1)-dimensional integral-differential equation [PDF]
arXiv, 2003 We represent the Fourier form of the dressing method, which is effective for construction of multidimensional integral-differential equations together with their solutions. Example of integrable (but non-physical) expansion of Intermediate Long Wave equation in (2+1)-dimensions is considered.
arxiv
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2023 Background. The purpose of this work is to study the 3-D scalar problem of scattering a plane wave from an inhomogeneous solid covered with an infinitely thin layer of graphene. Material and methods.
Aleksey A. Tsupak
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Analytical methods for solution of hypersingular and polyhypersingular integral equations [PDF]
arXiv, 2019 We propose a method for transformating linear and nonlinear hypersingular integral equations into ordinary differential equations. Linear and nonlinear polyhypersingular integral equations are transformed into partial differential equations. Well known that many types of differential equations can be solved in quadratures. So, we can receive analytical
arxiv
Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy
International Journal of Mathematics and Mathematical Sciences, 1991 A discussion is given of some of the properties of the functional Volterra Integral equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy. and of the corresponding multidimensional equation.
Li. G. Chambers
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Transformations between nonlocal and local integrable equations [PDF]
arXiv, 2017 Recently, a number of nonlocal integrable equations, such as the PT-symmetric nonlinear Schrodinger (NLS) equation and PT-symmetric Davey-Stewartson equations, were proposed and studied. Here we show that many of such nonlocal integrable equations can be converted to local integrable equations through simple variable transformations.
arxiv
Fractal and FractionalThis work studies an integro-fractional differential equation (I-FrDE) with a generalized symmetric singular kernel. The scientific approach in this study was to transform the integro-differential equation (I-DE) into a mixed integral equation (MIE) with
Sameeha A. Raad, Mohammed A. Abdou
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