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The integrable KdV6 equations: Multiple soliton solutions and multiple singular soliton solutions
Applied Mathematics and Computation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Yi, Cai, Xiao-Na, Xu, Hong-Xian
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Solitonic solutions and gravitational solitons: a brief introduction
2021In this work we intend to discuss the solitonic solutions of Einstein's field equations in vacuum by constructing the solution to N solitons and studying some aspects of it. In conclusion, it will be shown how the Kerr black hole can be interpreted as a soliton solution in the case of axial symmetry.
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Numerical solution of soliton bag models
Physical Review D, 1985We develop a new, efficient, and accurate method of obtaining numerical solutions for soliton bag models. By introducing additional differential equations to describe the integral constraints and eigenvalue conditions, and after a careful analysis of the asymptotic form of the solutions, we convert the equations of the soliton bag model in the mean ...
, Dodd, , Lohe
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Ward’s Solitons II: Exact Solutions
Canadian Journal of Mathematics, 1998AbstractIn a previous paper, we gave a correspondence between certain exact solutions to a (2 + 1)-dimensional integrable Chiral Model and holomorphic bundles on a compact surface. In this paper, we use algebraic geometry to derive a closed-form expression for those solutions and show by way of examples how the algebraic data which parametrise the ...
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Time-dependent Kaluza–Klein soliton solutions
Journal of Mathematical Physics, 1993Time-dependent generalizations of the standard static, spherically symmetric solutions of the empty Kaluza–Klein or (4+1) Einstein equations are considered herein. Such time-dependent solutions exist because Birkhoff’s theorem does not hold in (4+1) gravity.
Liu, Hongya +2 more
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New Classes of Toda Soliton Solutions
Communications in Mathematical Physics, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gesztesy, F., Renger, W.
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On soliton solutions of the Kaup–Kupershmidt equation. II. ‘Anomalous’ N-soliton solutions
Physica D: Nonlinear Phenomena, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multiple-soliton solutions of Einstein’s equations
Journal of Mathematical Physics, 1989Using the Belinsky–Zakharov generating technique and a flat metric as a seed, two- and four-soliton solutions of the Einstein vacuum equations for the cases of stationary axisymmetric, cylindrically symmetric, or plane symmetric gravitational fields are considered. Three- and five-parameter classes of exact solutions are obtained, some of which are new.
Economou, A., Tsoubelis, D.
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Exact soliton solutions for the core of dispersion-managed solitons
Physical Review E, 2003We consider the averaged dispersion-managed (DM) fiber system equation, which governs the dynamics of the core of the DM solitons. For a special case of such a system equation, we derive the exact soliton solutions using the Darboux transformation. Further, we discuss the interaction scenario between two neighboring solitons.
Xu, Z +4 more
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The soliton solutions and combined solutions of a high-dimensional wave soliton equation
Physica Scripta, 2022Abstract In this paper, a high-dimensional wave soliton equation is considered and the simple Hirota method and bilinear backlund transformation are applied to construct the new soliton solutions, lump soliton solutions, breather solutions and their combined solutions.
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