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On a transformation of integral equations
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yengibaryan, B. N., Yengibaryan, N. B.
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Bäklund transformations and singular integral equations
Physica A: Statistical Mechanics and its Applications, 1984A systematic method for deriving Bäcklund transformations for singular (linear) integral equations is presented. The method leads in a natural way to the Bäcklund transformations for the corresponding (integrable) nonlinear partial differential equations.
Quispel, G. R. W. +3 more
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Fractional oscillator equation – Transformation into integral equation and numerical solution
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tomasz Blaszczyk, Mariusz Ciesielski
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The integration of ordinary differential equations: factorization and transformations
Mathematics and Computers in Simulation, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Integration of the Schrödinger equation by canonical transformations
Physical Review A, 2001Owing to the operator nature of the quantum dynamical variables, classical canonical transformations for integrating the equations of motion cannot be extended to the quantum domain. In this paper, a general procedure is developed to construct the sequences of quantum canonical transformations for integrating the Schrodinger equations.
Gin-yih Tsaur, Jyhpyng Wang
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A Unitary Transform Related to Some Integral Equations
SIAM Journal on Mathematical Analysis, 1970The integral equations \[ F(x) = \frac{d}{{dx}}\int_0^x {J_0 [2\sqrt {k(x - t)} ]f(t)dt} \] and \[ G(x) = \frac{d}{{dx}}\int_x^\infty {J_0 [2\sqrt {k(t - x)} ]g(t)dt} \] are usually considered separately, and their solutions \[ f(x) = \frac{d}{{dx}}\int_0^x {I_0 [2\sqrt {k(x - t)} ]F(t)dt} \] and \[ g(x) = \frac{d} {{dx}}\int_x^\infty {I_0 [2\sqrt {k(t
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