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Journal articles on the topic 'Two soliton bound states'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Xu, Tao, Yong Chen, and Zhijun Qiao. "Multi-dark soliton solutions for the (2+1)-dimensional multi-component Maccari system." Modern Physics Letters B 33, no. 31 (November 10, 2019): 1950390. http://dx.doi.org/10.1142/s0217984919503901.

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Based on reduction of the KP hierarchy, the general multi-dark soliton solutions in Gram type determinant forms for the (2[Formula: see text]+[Formula: see text]1)-dimensional multi-component Maccari system are constructed. Especially, the two component coupled Maccari system comprising of two component short waves and single-component long waves are discussed in detail. Besides, the dynamics of one and two dark-dark solitons are analyzed. It is shown that the collisions of two dark-dark solitons are elastic by asymptotic analysis. Additionally, the two dark-dark solitons bound states are stud

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2

VELARDE, MANUEL G., ALEXANDER P. CHETVERIKOV, WERNER EBELING, DIRK HENNIG, and JOHN J. KOZAK. "ON THE MATHEMATICAL MODELING OF SOLITON-MEDIATED LONG-RANGE ELECTRON TRANSFER." International Journal of Bifurcation and Chaos 20, no. 01 (January 2010): 185–94. http://dx.doi.org/10.1142/s0218127410025508.

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We discuss here possible models for long-range electron transfer (ET) between a donor (D) and an acceptor (A) along an anharmonic (Morse–Toda) one-dimensional (1d)-lattice. First, it is shown that the electron may form bound states (solectrons) with externally, mechanically excited solitons in the lattice thus leading to one form of soliton-mediated transport. These solectrons generally move with supersonic velocity. Then, in a thermally excited lattice, it is shown that solitons can also trap electrons, forming similar solectron bound states; here, we find that ET based on hopping can be mode

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3

Zhong, Hui, and Bo Tian. "Stochastic Soliton Solutions of the High-Order Nonlinear Schrödinger Equation in the Optical Fiber with Stochastic Dispersion and Nonlinearity." Zeitschrift für Naturforschung A 69, no. 1-2 (February 1, 2014): 21–33. http://dx.doi.org/10.5560/zna.2013-0071.

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In this paper, the high-order nonlinear Schrödinger (HNLS) equation driven by the Gaussian white noise, which describes the wave propagation in the optical fiber with stochastic dispersion and nonlinearity, is studied. With the white noise functional approach and symbolic computation, stochastic one- and two-soliton solutions for the stochastic HNLS equation are obtained. For the stochastic one soliton, the energy and shape keep unchanged along the soliton propagation, but the velocity and phase shift change randomly because of the effects of Gaussian white noise. Ranges of the changes increas

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4

Yang, S. R. Eric. "Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences." Nanomaterials 9, no. 6 (June 14, 2019): 885. http://dx.doi.org/10.3390/nano9060885.

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An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar properties, e.g., the bulk-edge correspondence between the Zak phase and the existence of edge states, along with the presence of chiral boundary states, which are important for charge fractionalization. In polyacetylene, a fermion mass potential in the Dirac equation produces an excitation gap, and a twist in this scalar potential produces a zero-energy chiral so

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5

Huang, Guoxiang, Zhupei Shi, Xianxi Dai, and Ruibao Tao. "Two-Soliton Bound States in a Heisenberg Spin Chain." Communications in Theoretical Physics 16, no. 1 (July 1991): 93–96. http://dx.doi.org/10.1088/0253-6102/16/1/93.

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6

MANTOVANI-SARTI, VALENTINA, BYUNG-YOON PARK, and VICENTE VENTO. "THE SOLITON–SOLITON INTERACTION IN THE CHIRAL DILATON MODEL." International Journal of Modern Physics A 28, no. 27 (October 30, 2013): 1350136. http://dx.doi.org/10.1142/s0217751x13501364.

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We study the interaction between two B = 1 states in the Chiral Dilaton Model where baryons are described as nontopological solitons arising from the interaction of chiral mesons and quarks. By using the hedgehog solution for B = 1 states we construct, via a product ansatz, three possible B = 2 configurations to analyse the role of the relative orientation of the hedgehog quills in the dynamics of the soliton–soliton interaction and investigate the behavior of these solutions in the range of long/intermediate distance. One of the solutions is quite binding due to the dynamics of the π and σ fi

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7

Chai, Jun, Bo Tian, Yu-Feng Wang, Wen-Rong Sun, and Yun-Po Wang. "Conservation Laws and Mixed-Type Vector Solitons for the 3-Coupled Variable-Coefficient Nonlinear Schrödinger Equations in Inhomogeneous Multicomponent Optical Fibre." Zeitschrift für Naturforschung A 71, no. 6 (June 1, 2016): 525–39. http://dx.doi.org/10.1515/zna-2016-0019.

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AbstractIn this article, the propagation and collision of vector solitons are investigated from the 3-coupled variable-coefficient nonlinear Schrödinger equations, which describe the amplification or attenuation of the picosecond pulses in the inhomogeneous multicomponent optical fibre with different frequencies or polarizations. On the basis of the Lax pair, infinitely-many conservation laws are obtained. Under an integrability constraint among the variable coefficients for the group velocity dispersion (GVD), nonlinearity and fibre gain/loss, and two mixed-type (2-bright-1-dark and 1-bright-

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8

Wang, Guomei, Guangwei Chen, Wenlei Li, Chao Zeng, and Wei Zhao. "Observation of evolution dynamics from bound states to single-pulse states in a passively mode-locked fiber laser." Modern Physics Letters B 33, no. 09 (March 30, 2019): 1950103. http://dx.doi.org/10.1142/s0217984919501033.

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We report what is, to our knowledge, the first experimental observation of the ultrafast evolution dynamics from bound states (BSs) to single-pulse states (SPSs) by using the dispersive Fourier-transform (DFT) technique. The evolutions from three categories of initial BSs to SPSs are spectrally resolved in real time. Usually, accompanied by complex soliton–soliton interaction and competition, one of the two bound pulses weakens to disappearance, and the other one evolves into SPS. During the transition, the two bound pulses ordinarily depart away from each other with complex changes of relativ

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9

Liu, Lei, Bo Tian, Xiao-Yu Wu, and Yu-Qiang Yuan. "Vector Dark Solitons for a Coupled Nonlinear Schrödinger System with Variable Coefficients in an Inhomogeneous Optical Fibre." Zeitschrift für Naturforschung A 72, no. 8 (August 28, 2017): 779–87. http://dx.doi.org/10.1515/zna-2017-0148.

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AbstractStudied in this paper are the vector dark solitons for a coupled nonlinear Schrödinger system with variable coefficients, which can be used to describe the pulse simultaneous propagation of the M-field components in an inhomogeneous optical fibre, where M is a positive integer. When M=2, under the integrable constraint, we construct the nondegenerate N-dark-dark soliton solutions in terms of the Gramian through the Kadomtsev–Petviashvili hierarchy reduction. With the help of analytic analysis, a vector one soliton with varying amplitude and velocity is studied. Interactions and bound s

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10

Zhang, Liqiang, Zhiyong Pan, Zhuang Zhuo, and Yunzheng Wang. "Three Multiple-Pulse Operation States of an All-Normal-Dispersion Dissipative Soliton Fiber Laser." International Journal of Optics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/169379.

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Multiple-pulse operation states of an all-normal-dispersion Yb-doped double-clad dissipative soliton fiber laser are investigated in this paper. The proposed laser can deliver harmonic mode-locked pulses, bound states of dissipative solitons, and dual-wavelength dual-pulses. Stable second-harmonic and third-harmonic mode-locked pulse trains are obtained with the output power of 1.39 W and 1.46 W, respectively, and the corresponding single pulse energies are 12.1 nJ and 8.5 nJ. With the adjustment of pump power and the wave plates, the fiber laser generates bound states of two or three dissipat

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11

Qadir, Muhammad Irfan, and Usama Tahir. "Bound states of atomic Josephson vortices." Canadian Journal of Physics 95, no. 4 (April 2017): 336–39. http://dx.doi.org/10.1139/cjp-2016-0599.

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We study the existence and stability of the bound state Josephson vortices solution in two parallel quasi one-dimensional coupled Bose–Einstein condensates. The system can be elucidated by linearly coupled Gross–Pitaevskii equations. The purpose of this study is to investigate the effects of altering the strength of coupling between the two condensates over the stability of the bound-state Josephson vortices. It is found that the stability of bound-state Josephson vortices depends on the value of coupling strength. However, at a critical value of coupling parameter, the Josephson vortices solu

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12

Burzlaff, J. "The soliton number of optical soliton bound states for two special families of input pulses." Journal of Physics A: Mathematical and General 21, no. 2 (January 21, 1988): 561–66. http://dx.doi.org/10.1088/0305-4470/21/2/034.

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13

GANDENBERGER, GEORG M. "TRIGONOMETRIC S MATRICES, AFFINE TODA SOLITONS AND SUPERSYMMETRY." International Journal of Modern Physics A 13, no. 26 (October 20, 1998): 4553–90. http://dx.doi.org/10.1142/s0217751x98002195.

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Using [Formula: see text]- and [Formula: see text]-invariant R matrices we construct exact S matrices in two-dimensional space–time. These are conjectured to describe the scattering of solitons in affine Toda field theories. In order to find the spectrum of soliton bound states we examine the pole structure of these S matrices in detail. We also construct the S matrices for all scattering processes involving scalar bound states. In the last part of this paper we discuss the connection of these S matrices with minimal N=1 and N = 2 super-symmetric S matrices. In particular we comment on the fol

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14

Dmitriev, Sergey V., and Takeshi Shigenari. "Short-lived two-soliton bound states in weakly perturbed nonlinear Schrödinger equation." Chaos: An Interdisciplinary Journal of Nonlinear Science 12, no. 2 (June 2002): 324–31. http://dx.doi.org/10.1063/1.1476951.

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15

Shao, Li, Yun-Long Wu, and Qing Ye. "Anomalous Propagation Characteristics of Airy Beam in Nonlinear Kerr Media." Crystals 11, no. 8 (July 28, 2021): 879. http://dx.doi.org/10.3390/cryst11080879.

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The propagation characteristics of a single Airy beam in nonlinear Kerr media were numerically investigated by utilizing the split-step Fourier transform method. We show that in addition to normal breathing solitons, the anomalous bound states of Airy spatial solitons can also be formed, which are similar to the states formed in the interaction between two Airy beams in nonlinear media. This quasi-equilibrium state is formed by the interaction of the main soliton beam and side lobes of Airy beam due to their different propagation trajectories in the nonlinear media. Moreover, it has been shown

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16

Ren, Bo. "Characteristics of the Soliton Molecule and Lump Solution in the 2 + 1 -Dimensional Higher-Order Boussinesq Equation." Advances in Mathematical Physics 2021 (April 9, 2021): 1–7. http://dx.doi.org/10.1155/2021/5545984.

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The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2 + 1 -dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2 + 1 -dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation are constructed. The soliton molecule does not exist for the usual 2 + 1 -dimensional Boussinesq equation. As a special kind of rational solution, the lump wave is localized in all

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17

Feng, Yu-Jie, Yi-Tian Gao, Ting-Ting Jia, and Liu-Qing Li. "Soliton interactions of a variable-coefficient three-component AB system for the geophysical flows." Modern Physics Letters B 33, no. 29 (October 20, 2019): 1950354. http://dx.doi.org/10.1142/s0217984919503548.

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Geophysical flows consist of the large-scale motions of the ocean and/or atmosphere. Researches on the geophysical flows reveal the mechanisms for the transport and redistribution of energy and matter. Investigated in this paper is a variable-coefficient three-component AB system for the baroclinic instability processes in geophysical flows. With respect to the three wave packets as well as the correction to the mean flow, bilinear forms are obtained, and one-, two- and [Formula: see text]-soliton solutions are derived under some coefficient constraints via the Hirota method. Soliton interacti

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18

Qadir, Muhammad Irfan, and Tehseen Zoma. "Symmetric bound states of Josephson vortices in BEC." Canadian Journal of Physics 96, no. 2 (February 2018): 208–12. http://dx.doi.org/10.1139/cjp-2017-0269.

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A system of two parallel coupled cigar-shaped Bose–Einstein condensates is considered in an effectively one-dimensional limit. The dynamics of the system is characterized by a pair of coupled nonlinear Gross–Pitaevskii equations. In particular, the existence and stability of symmetric bound states of Josephson vortices are investigated. It is realized that the symmetric bound state Josephson vortices solution persists stably in its whole domain of existence for the coupling strength. Nevertheless, the bound states solution converts into a dark soliton at a critical value of coupling parameter.

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19

ZHENG, WEIHONG, CHRIS J. HAMER, RAJIV R. P. SINGH, SIMON TREBST, and HARTMUT MONIEN. "LINKED CLUSTER SERIES EXPANSIONS FOR TWO-PARTICLE STATES IN QUANTUM LATTICE MODELS." International Journal of Modern Physics B 17, no. 28 (November 10, 2003): 5011–20. http://dx.doi.org/10.1142/s0217979203020144.

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We have developed strong-coupling series expansion methods to study the two-particle spectra in quantum lattice models. The properties of bound states and multiparticle excitations can reveal important information about the dynamics of a given model. At the heart of this method lies the calculation of an effective Hamiltonian in the two-particle subspace. We use an orthogonal transformation to perform this block diagonalising, and find that maintaining orthogonality is crucial for cases where the ground state and the two-particle subspace have identical quantum numbers. The two-particle Schröd

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20

Konyukhov, Andrey I. "Transformation of Eigenvalues of the Zakharov–Shabat Problem under the Effect of Soliton Collision." Izvestiya of Saratov University. New series. Series: Physics 20, no. 4 (2020): 248–57. http://dx.doi.org/10.18500/1817-3020-2020-20-4-248-257.

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Background and Objectives: The Zakharov–Shabat spectral problem allows to find soliton solutions of the nonlinear Schrodinger equation. Solving the Zakharov–Shabat problem gives both a discrete set of eigenvalues λj and a continuous one. Each discrete eigenvalue corresponds to an individual soliton with the real part Re(λj) providing the soliton velocity and the imaginary part Im(λj) determining the soliton amplitude. Solitons can be used in optical communication lines to compensate both non-linearity and dispersion. However, a direct use of solitons in return-to-zero signal encoding is inhibi

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21

Li, Z. J., H. B. Xu, and K. L. Yao. "The Energy Band Structure of Polyacene with Soliton Excitation." Modern Physics Letters B 11, no. 11 (May 10, 1997): 477–83. http://dx.doi.org/10.1142/s021798499700058x.

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Starting from the extensional Su–Schrieffer–Heeger model taking into account the effects of interchain coupling, we have studied the energy spectra and electronic states of soliton excitation in polyacene. The dimerized displacement u0 is found to be similar to the case of trans-polyacetylene, and equals to 0.04 Å. The energy-band gap is 0.38 eV, in agreement with the results derived by other authors. Two new bound electronic states have been found in the conduction band and in the valence band, which is different from the one of trans-polyacetylene. There exists two degenerate soliton states

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22

Vakhnenko, V. O., and E. J. Parkes. "Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation." Advances in Mathematical Physics 2016 (2016): 1–39. http://dx.doi.org/10.1155/2016/2916582.

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A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE) as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE), by a change of independent variables. The VPE has anN-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the cor

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23

GOBBI, CARLO, SIGFRIDO BOFFI, and DMITRI E. KHARZEEV. "PRODUCTION OF CHARMONIUM-NUCLEON BOUND STATES IN THE TOPOLOGICAL SOLITON MODEL." Modern Physics Letters A 09, no. 32 (October 20, 1994): 3035–40. http://dx.doi.org/10.1142/s0217732394002860.

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The photo- and electro-production cross-sections of charmonium-nucleon bound states on protons are calculated in the framework of the topological soliton model. The size of these cross-sections is predicted too small to be detected using present experimental facilities.

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24

He, Jun-Rong, and Lin Yi. "Formations of n-order two-soliton bound states in Bose–Einstein condensates with spatiotemporally modulated nonlinearities." Physics Letters A 378, no. 16-17 (March 2014): 1085–90. http://dx.doi.org/10.1016/j.physleta.2014.01.050.

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25

JÜRGENSEN, HELMUT, and PAULINE KRAAK. "SOLITON AUTOMATA BASED ON TREES." International Journal of Foundations of Computer Science 18, no. 06 (December 2007): 1257–70. http://dx.doi.org/10.1142/s0129054107005303.

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Soliton automata are a mathematical model for molecular switching devices. For even the simple case of soliton automata based on trees the behaviour is not known. For example, only two examples of such soliton automata were known the transition monoid of which is not the symmetric group on the set of states; and in these cases the transition monoid is the corresponding alternating group. We establish new bounds on the number of states of a tree-based soliton automaton and a sufficient condition for when the transition monoid of such a soliton automaton consists only of even permutations of the

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26

Mahmood, M. F., W. W. Zachary, and T. L. Gill. "Bound States of Envelope Solitons in Coupled Nonlinear Schrödinger Equations." Journal of Nonlinear Optical Physics & Materials 06, no. 01 (March 1997): 49–53. http://dx.doi.org/10.1142/s0218863597000046.

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Interaction of strongly and weakly overlapping solitons of two independent modes is analyzed in the framework of a system of coupled nonlinear Schrödinger equations with oscillating terms. A Hamiltonian formulation is employed. Our analysis reveals that the solitons form a strongly bound state with their centers coincident and weakly bound states with their centers separated from each other.

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27

Kevrekidis, P. G., B. A. Malomed, and A. R. Bishop. "Bound states of two-dimensional solitons in the discrete nonlinear Schrödinger equation." Journal of Physics A: Mathematical and General 34, no. 45 (November 6, 2001): 9615–29. http://dx.doi.org/10.1088/0305-4470/34/45/302.

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28

Akylas, T. R., Guenbo Hwang, and Jianke Yang. "From non-local gap solitary waves to bound states in periodic media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2137 (August 31, 2011): 116–35. http://dx.doi.org/10.1098/rspa.2011.0341.

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Solitary waves in one-dimensional periodic media are discussed by employing the nonlinear Schrödinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become non-local owing to the presence of growing tails of exponentially small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such non-local solitary waves, high-order

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29

He, Y. J., Boris A. Malomed, Dumitru Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang. "Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg–Landau equations with a linear potential." Optics Letters 34, no. 19 (September 25, 2009): 2976. http://dx.doi.org/10.1364/ol.34.002976.

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30

Yun, Ling. "Observations of bound states of two and three dissipative solitons in a figure-eight laser in a normal dispersion regime." Laser Physics 23, no. 4 (March 5, 2013): 045106. http://dx.doi.org/10.1088/1054-660x/23/4/045106.

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31

LU DING-WEI, SUN XIN, FU ROU-LI, and LIU JIE. "ELECTRONIC BOUND STATES OF CHARGED SOLITON." Acta Physica Sinica 39, no. 2 (1990): 289. http://dx.doi.org/10.7498/aps.39.289.

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32

Oh, Yongseok, and Byung-Yoon Park. "Energy levels of soliton–heavy-meson bound states." Physical Review D 51, no. 9 (May 1, 1995): 5016–29. http://dx.doi.org/10.1103/physrevd.51.5016.

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33

Kockaert, P., and M. Haelterman. "Stability and symmetry breaking of soliton bound states." Journal of the Optical Society of America B 16, no. 5 (May 1, 1999): 732. http://dx.doi.org/10.1364/josab.16.000732.

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34

Milián, C., D. E. Ceballos-Herrera, D. V. Skryabin, and A. Ferrando. "Soliton-plasmon resonances as Maxwell nonlinear bound states." Optics Letters 37, no. 20 (October 5, 2012): 4221. http://dx.doi.org/10.1364/ol.37.004221.

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35

Rho, Mannque, D. O. Riska, and N. N. Scoccola. "Charmed baryons as soliton-D meson bound states." Physics Letters B 251, no. 4 (November 1990): 597–602. http://dx.doi.org/10.1016/0370-2693(90)90802-d.

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36

Bogdan, M. M., and O. V. Charkina. "Dynamics of bound soliton states in regularized dispersive equations." Low Temperature Physics 34, no. 7 (July 2008): 564–70. http://dx.doi.org/10.1063/1.2957009.

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37

Latas, S. C. V., and M. F. S. Ferreira. "Self-frequency shift effect on dissipative soliton bound states." Applied Physics B 105, no. 4 (October 11, 2011): 863–69. http://dx.doi.org/10.1007/s00340-011-4736-4.

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38

Kamburova, R. S., and M. T. Primatarowa. "Bound Soliton–Defect Spin States in Anisotropic Ferromagnetic Chains." Journal of Physics: Conference Series 1762, no. 1 (February 1, 2021): 012020. http://dx.doi.org/10.1088/1742-6596/1762/1/012020.

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39

Kälbermann, G. "Decay to bound states of a soliton in a well." Chaos, Solitons & Fractals 12, no. 4 (January 3, 2001): 625–29. http://dx.doi.org/10.1016/s0960-0779(00)00037-0.

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40

Latas, Sofia C. V., Mário F. S. Ferreira, and Augusto S. Rodrigues. "Bound states of plain and composite pulses: Multi-soliton solutions." Optical Fiber Technology 11, no. 3 (July 2005): 292–305. http://dx.doi.org/10.1016/j.yofte.2004.12.003.

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41

Afanasjev, V. V., and N. Akhmediev. "Soliton interaction and bound states in amplified-damped fiber systems." Optics Letters 20, no. 19 (October 1, 1995): 1970. http://dx.doi.org/10.1364/ol.20.001970.

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42

Haelterman, M., S. Trillo, and P. Ferro. "Multiple soliton bound states and symmetry breaking in quadratic media." Optics Letters 22, no. 2 (January 15, 1997): 84. http://dx.doi.org/10.1364/ol.22.000084.

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43

Buryak, Alexander V. "Stationary soliton bound states existing in resonance with linear waves." Physical Review E 52, no. 1 (July 1, 1995): 1156–63. http://dx.doi.org/10.1103/physreve.52.1156.

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44

Hołyst, J. A., and H. Benner. "Soliton-magnon bound states in TMMC above and below TN." Journal of Magnetism and Magnetic Materials 140-144 (February 1995): 1969–70. http://dx.doi.org/10.1016/0304-8853(94)00717-9.

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45

Piette, Bernard, and Wojtek J. Zakrzewski. "Skyrmion model in 2 + 1 dimensions with soliton bound states." Nuclear Physics B 393, no. 1-2 (March 1993): 65–78. http://dx.doi.org/10.1016/0550-3213(93)90237-j.

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46

Basu-Mallick, B., Tanaya Bhattacharyya, and Diptiman Sen. "Bound and anti-bound soliton states for a quantum integrable derivative nonlinear Schrödinger model." Physics Letters A 325, no. 5-6 (May 2004): 375–80. http://dx.doi.org/10.1016/j.physleta.2004.04.010.

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47

Haelterman, M., and A. Sheppard. "Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media." Physical Review E 49, no. 4 (April 1, 1994): 3376–81. http://dx.doi.org/10.1103/physreve.49.3376.

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48

Giachetti, R., and E. Sorace. "Two fermion relativistic bound states." Journal of Physics A: Mathematical and General 38, no. 6 (January 27, 2005): 1345–70. http://dx.doi.org/10.1088/0305-4470/38/6/012.

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49

Britto-Pacumio, Ruth, Andrew Strominger, and Anastasia Volovich. "Two-black-hole bound states." Journal of High Energy Physics 2001, no. 03 (March 29, 2001): 050. http://dx.doi.org/10.1088/1126-6708/2001/03/050.

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50

Yennie, Donald R. "Two-body QED bound states." Zeitschrift für Physik C Particles and Fields 56, S1 (March 1992): S13—S23. http://dx.doi.org/10.1007/bf02426770.

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