Journal of Mathematical Physics
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Separation of the Interaction Potential into Two Parts in Treating Many-Body Systems. I. General Theory and Applications to Simple Fluids with Short-Range and Long-Range ForcesSystematic methods are developed for investigating the correlation functions and thermodynamic properties of a classical system of particles interacting via a pair potential v(r) = q(r) + w(r). The method is then applied to the case in which w(r) is a ``Kac potential'' w(r, γ) = γvφ(γr) (v the dimensionality of the space) whose range γ−1 is very long compared to the range of q(r). Our work... ... hiện toàn bộ
Journal of Mathematical Physics - Tập 6 Số 8 - Trang 1282-1298 - 1965
Soliton solutions to coupled higher-order nonlinear Schrödinger equationsA set of coupled higher-order nonlinear Schrödinger equations, which describe electromagnetic pulse propagation in coupled optical waveguides, is formulated in terms of an eigenvalue problem. Using that result, the inverse scattering problem is solved and explicit soliton solutions are found. Additionally, linear coupling terms are studied systematically.
Journal of Mathematical Physics - Tập 33 Số 3 - Trang 1208-1215 - 1992
A restricted Bäcklund transformationThe Bäcklund transformation provides a mathematical tool which displays the interaction of solitons. Here a simple, systematic Bäcklund formalism is introduced which permits the explicit construction of these transformations for a restricted class of nonlinear wave equations. Traditionally a Bäcklund transformation has been viewed as a transformation of a solution surface of a partial diff... ... hiện toàn bộ
Journal of Mathematical Physics - Tập 14 Số 12 - Trang 1817-1828 - 1973
New reductions of the Kadomtsev–Petviashvili and two-dimensional Toda lattice hierarchies via symmetry constraintsNew types of reductions of the Kadomtsev–Petviashvili (KP) hierarchy and the two-dimensional Toda lattice (2DTL) hierarchy are considered on the basis of Sato’s approach. Within this approach these hierarchies are represented by infinite sets of equations for potentials u1,u2,u3,..., of pseudodifferential operators and their eigenfunctions ψ and adjoint eigenfunctions ψ*. The KP and the 2D... ... hiện toàn bộ
Journal of Mathematical Physics - Tập 33 Số 11 - Trang 3676-3686 - 1992
Multicomponent integrable reductions in the Kadomtsev–Petviashvilli hierarchyNew types of reductions of the Kadomtsev–Petviashvili (KP) hierarchy are considered on the basis of Sato’s approach. Within this approach the KP hierarchy is represented by infinite sets of equations for potentials u2,u3,..., of pseudodifferential operators and their eigenfunctions Ψ and adjoint eigenfunctions Ψ*. The KP hierarchy was studied under constraints of the following type (∑ni=1 ... ... hiện toàn bộ
Journal of Mathematical Physics - Tập 34 Số 4 - Trang 1429-1446 - 1993
A homogeneous Hilbert problem for the Kinnersley–Chitre transformations of electrovac space-timesThe homogeneous Hilbert problem which we recently formulated for Kinnersley–Chitre transformations of vacuum spacetimes is here generalized to handle transformations of electrovac spacetimes. This provides in particular a simple derivation of our previously published integral equation.
Journal of Mathematical Physics - Tập 21 Số 6 - Trang 1418-1422 - 1980
A homogeneous Hilbert problem for the Kinnersley–Chitre transformationsA homogeneous Hilbert (Riemann) problem (HHP) is introduced for carrying out the Kinnersley–Chitre transformations of the set V of all axially symmetric stationary vacuum spacetimes, and the spacetimes which are like the axially symmetric stationary ones except that both Killing vectors are spacelike. A proof, which is independent of the Kinnersley–Chitre formalism, establishes that the HH... ... hiện toàn bộ
Journal of Mathematical Physics - Tập 21 Số 5 - Trang 1126-1140 - 1980
Diffuse Transmission of Light from a Central Source through an Inhomogeneous Spherical Shell with Isotropic ScatteringA partial-differential-integral equation is derived in this paper for the angular distribution of the radiation which is diffusely transmitted through an inhomogeneous, isotropically scattering, spherical shell when there is a constant net flux of radiation normally incident on the inner surface. An equation is also derived for the strength of the diffusely reflected radiation when the she... ... hiện toàn bộ
Journal of Mathematical Physics - Tập 9 Số 6 - Trang 909-912 - 1968
Exact semiclassical expansions for one-dimensional quantum oscillatorsA set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also... ... hiện toàn bộ
Journal of Mathematical Physics - Tập 38 Số 12 - Trang 6126-6184 - 1997
Open perturbation and the Riccati equation: Algebraic determination of the quartic anharmonic oscillator energies and eigenfunctionsAn algebraic procedure is proposed for the analytical solution of Schrödinger equations that can be viewed as a factorizable equation with an additional potential V(x). Once V(x) has been expanded in a series of suitable x-basis functions u=u(x), which are specific to each factorization type, the solution of the Riccati equation associated with the given equation is performed by means of a... ... hiện toàn bộ
Journal of Mathematical Physics - Tập 38 Số 11 - Trang 5483-5492 - 1997
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