Results 251 to 260 of about 2,326,383 (287)

Bäklund transformations and singular integral equations

Physica A: Statistical Mechanics and its Applications, 1984
A 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., Nijhoff, F. W., Capel, H. W., van der Linden, J.   +3 more
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Fractional oscillator equation – Transformation into integral equation and numerical solution

Applied Mathematics and Computation, 2015
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Tomasz Blaszczyk, Mariusz Ciesielski
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Integration of the Schrödinger equation by canonical transformations

Physical Review A, 2001
Owing 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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The integration of ordinary differential equations: factorization and transformations

Mathematics and Computers in Simulation, 2001
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Integral Transforms and Differential Equations

1999
The discussion in Chap. 15 introduced a general method of solving differential equations by power series—also called the Frobenius method—which gives a solution that converges within a circle of convergence. In general, this circle of convergence may be small; however, the function represented by the power series can be analytically continued using ...
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A Unitary Transform Related to Some Integral Equations

SIAM Journal on Mathematical Analysis, 1970
The 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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Integral Transforms and Dual Integral Equations to Solve Heat Equation with Mixed Conditions

International Journal of Open Problems in Computer Science and Mathematics, 2014
The paper is devoted to determine the solution of the non-stationary heat equation in a non axial symmetric cylindrical coordinates subject to mixed discontinuous boundary conditions of the second kind and third kinds, with the aid of a finite Fourier transform and dual integral equations method. The solution of the given mixed problem is introduced to
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Nonlinear Transformations and Integrable Evolution Equations

Fortschritte der Physik/Progress of Physics, 1983
The transformation properties of the partial differential equations integrable by the inverse scattering transform method are considered. It is shown that the nonlinear transformations characteristic to the integrable equations (symmetry groups, Backlund-transformations) and integrable equations themselves are contained in certain universal nonlinear ...
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Linear integral transformations and hierarchies of integrable nonlinear evolution equations

Physica D: Nonlinear Phenomena, 1988
Integrable hierarchies of nonlinear evolution equations are investigated on the basis of linear integral equations. These are (Riemann-Hilbert type of) integral transformations which leave invariant an infinite sequence of ordinary differential matrix equations of increasing order in an (indefinite) parameter k.
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The Boussinesq equation as a source of equations integrable by the spectral transform

Nonlinearity, 1997
Summary: Integrable and nonlinear partial differential equations are obtained from the Boussinesq equation by means of an asymptotic reduction method based on Fourier decomposition and spatio-temporal rescaling. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs are derived, applying the same ...
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