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Boundary conditions for integrable equations
Functional Analysis and Its Applications, 1987zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1994
We first consider an expository linear example: with conditions given as: γ, β 1,, and β 2 are assumed constants here although they can be functions of x with minor modifications to the procedure given. In decomposition format we have Lu + Ru = 0 or L−1Lu = I:−L−1 Ru or where is a two-fold pure integration with respect to x.
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We first consider an expository linear example: with conditions given as: γ, β 1,, and β 2 are assumed constants here although they can be functions of x with minor modifications to the procedure given. In decomposition format we have Lu + Ru = 0 or L−1Lu = I:−L−1 Ru or where is a two-fold pure integration with respect to x.
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Boundary Value Problems With Integral Conditions
AIP Conference Proceedings, 2011The weakly perturbed nonlinear boundary value problems (BVP) for almost linear systems of ordinary differential equations (ODE) are considered. We assume that the nonlinear part contain an additional function, which defines the perturbation as singular. Then the Poincare method is not applicable. The problem of existence, uniqueness and construction of
L. I. Karandzhulov +4 more
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On a boundary value problem with integral boundary conditions
Differential Equations, 2015We study the existence of positive solutions of second-order ordinary differential equations with integral boundary conditions. The result generalizes the conditions obtained in [1] for the existence of positive solutions.
A. Ya. Lepin, L. A. Lepin
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Improved boundary integral method for inviscid boundary condition applications
AIAA Journal, 1993The potential part of an unsteady, incompressible, viscous flow is treated by means of a boundary integral method. Discretizing the surface of an object in form of panels, imposing inviscid boundary conditions (no flow through wall) and enforcing conservation of circulation leads to a problem which is not uniquely solvable but numerically ill-posed.
Koumoutsakos, P., Leonard, A.
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Integrable Boundary Conditions of the Modified Volterra Model
Journal of the Physical Society of Japan, 1997Summary: New boundary conditions of the so-called ``modified Volterra model'', which is described by a set of the nonlinear differential-difference equations, are presented. In accordance with the methods developed by Sklyanin, these conditions are shown to be integrable, including the simply truncated open-end case.
Kajinaga, Yasumasa, Wadati, Miki
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Integrable boundary conditions for many-component burgers equations
Mathematical Notes, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Svinolupov, S. I., Khabibullin, I. T.
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Boundary conditions for integrable quantum systems
Journal of Physics A: Mathematical and General, 1988A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open quantum chains with appropriate boundary terms in the Hamiltonian.
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Boundary conditions of Feynman path integrals
Nuclear Physics, 1966Abstract Feynman path integral expressions for transition matrix elements between bare vacua are derived for scalar and spinor fields. Proper boundary conditions are used to avoid the usual somewhat artificial iϵ prescriptions of previous authors.
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Second-order boundary value problems with integral boundary conditions
Nonlinear Analysis: Theory, Methods & Applications, 2009The author studies the existence of positive solutions of the solutions of the second-order boundary value problem \[ y'' = f(t, y(t)), \quad 0 < t < 1, \] \[ y(0) - ay'(0) = \int_0^1 \! g_0(s) y(s) \, ds, \] \[ y(1) - by'(1) = \int_0^1 \! g_1(s) y(s) \, ds, \] where \(f:[0, 1] \times \mathbb{R} \to \mathbb{R}\) and \(g_0, g_1 : [0, 1] \to [0, +\infty)\
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