Results 11 to 20 of about 181,927 (288)
Some Schemata for Applications of the Integral Transforms of Mathematical Physics
Mathematics, 2019 In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating ...
Yuri Luchko
doaj +3 more sources
Novel Bäcklund Transformations for Integrable Equations
Mathematics, 2022 In this paper, we construct a new matrix partial differential equation having a structure and properties which mirror those of a matrix fourth Painlevé equation recently derived by the current authors. In particular, we show that this matrix equation admits an auto-Bäcklund transformation analogous to that of this matrix fourth Painlevé equation.
Pilar Ruiz Gordoa, Andrew Pickering
openaire +3 more sources
Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’
Complexity, 2023 The goal of this study is to suggest a new general triple integral transform known as Gamar transform. Next, we compare the current transform to a number of existing triple integral transforms such as those by Laplace, Sumudu, Elzaki, Aboodh, and Laplace–
Abdelilah Kamal H. Sedeeg
doaj +1 more source
Bäcklund transformations between four Lax-integrable 3D equations [PDF]
Journal of Nonlinear Mathematical Physics, 2021 We show that four Lax-integrable 3D differential equations are related via B cklund transformations.
Morozov, Oleg I., Pavlov, Maxim V.
openaire +2 more sources
Polyconvolution of Hartley integral transforms $H_2$ and integral equations
Journal of Integral Equations and Applications, 2020 The authors introduce a polyconvolution \(\ast(f,g,h)(x)\) of functions \(f,g\) and \(h\) for the Hartley integral transform \(H_2\). It is shown that the polyconvolution satisfies the factorization equality \[ H_2(f\ast_2 g)(y)=(H_2f)(y)(H_2g)(y)(H_2h)(y),\qquad \forall y\in \mathbb R. \] The existence of the polyconvolution in the space \(L_1(\mathbb
Khoa, Nguyen Minh, Thang, Tran Van
openaire +3 more sources
An approximation method for the solution of nonlinear integral equations [PDF]
, 2006 A Chebyshev collocation method has been presented to solve nonlinear integral equations in terms of Chebyshev polynomials. This method transforms the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations ...
Akyuz-Dascioglu, A, Yaslan, HC
core +3 more sources
A novel integral transform operator and its applications [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2023 The proposed study is focused to introduce a novel integral transform op-erator, called Generalized Bivariate (GB) transform. The proposed trans-form includes the features of the recently introduced Shehu transform, ARA transform, and Formable transform.
Sh. Arora, A. Pasrija
doaj +1 more source
Bäcklund transformations for integrable lattice equations [PDF]
Journal of Physics A: Mathematical and Theoretical, 2008 We give new Backlund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of two other kinds. Specifically, it is found that some equations admit additional auto-BTs (with Backlund parameter),
openaire +2 more sources
Application of wavelets to singular integral scattering equations [PDF]
, 2004 The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques.
B. M. Kessler +10 more
core +1 more source
Multicomponent integrable wave equations: I. Darboux-dressing transformation [PDF]
Journal of Physics A: Mathematical and Theoretical, 2007 The Darboux-Dressing Transformations are applied to the Lax pair associated to systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both bright and dark soliton solutions. The general formalism is set up and the relevant equations are explicitly solved. Several instances of multicomponent wave equations of
Degasperis, A., Lombardo, S.
openaire +6 more sources