“…ABSTRACT: In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. …”
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“…We present the unified method and use it to integrate the ion sound and Langmuir waves (ISLW) model to retrieve optical soliton solutions. Some new dynamical optical solitons involving the combo of rational, trigonometric, and hyperbolic function solutions are added in this study. …”
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“…These considerations also determine the charge lattice of BPS soliton states, which proves to be a universal modulus-independent lattice when the charges are defined to be the canonical charges corresponding to the quantum supergravity symmetry groups.…”
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“…By numerically solving Maxwell’s equations, we find a soliton-like family of still azimuthal doughnuts, which we further study through an adiabatic perturbative theory that describes soliton evaporation in lossy media or condensation in actively pumped materials. …”
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“…After the initial observation by John Scott Russell of a solitary wave in a canal, his insightful laboratory experiments and the subsequent theoretical work of Boussinesq, Rayleigh and Korteweg and de Vries, interest in solitary waves in fluids lapsed until the mid 1960's with the seminal paper of Zabusky and Kruskal describing the discovery of the soliton. This was followed by the rapid development of the theory of solitons and integrable systems. …”
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“…As a proof-of-concept demonstration, the PARTI system is applied to study the dynamic waveforms of slowly evolved dissipative Kerr solitons in an ultrahigh-Q microresonator. Two 1.5-ns-long comprehensive evolution portraits are reconstructed with 740 fs resolution and dissipative Kerr soliton transition dynamics, in which a multiplet soliton state evolves into a stable singlet soliton state, are depicted.…”
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“…Here, we demonstrate that the optical spectrum of a soliton microcomb generated in a microresonator can be extended by bichromatic pumping: one laser with a wavelength in the anomalous dispersion regime of the microresonator generates a bright soliton microcomb while another laser in the normal dispersion regime both compensates the thermal effect of the microresonator and generates a repetition-rate-synchronized second frequency comb. …”
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“…Through adjusting the distance between the grating pair, mode-locked pulses corresponding to different dispersion regimes can be realized, which typically range from soliton state in the anomalous dispersion regime to the dissipative soliton format in the normal dispersion regime. …”
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“…The method for constructing multi-soliton solutions on a given string background is briefly discussed.…”
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“…In this way the intersection properties can be represented in terms of a soliton graph that forms a generalized Z_{n+k+1} symmetric McKay quiver. …”
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“…Here, by using a powerful class of micro-comb called soliton crystals, we achieve ultra-high data transmission over 75 km of standard optical fibre using a single integrated chip source. …”
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“…We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. …”
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“…As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. …”
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“…which are consistent with chiral soliton models and indications from lattice estimates. …”
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“…The observed vortex phase segregation implies the existence of the soliton solution for the vortex density in the finite superconductors and establishes a new class of nonlinear systems that exhibit the soliton phenomenon.…”
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“…We also briefly discuss their vacuum structure, Backlund transformations, and soliton solutions.…”
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“…Through the application of these techniques, we obtain numerous previously unreported novel dynamic optical soliton solutions in mixed hyperbolic, trigonometric, and rational forms of the governing model. …”
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“…Optical soliton solutions are recovered for magneto–optic waveguides that maintains anti–cubic form of nonlinear refractive index. …”
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“…This is expected in chiral soliton models, which also predicted the existence of new exotic baryons that may recently have been observed. …”
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“…In particular, by restricting our asymptotic result to solutions whose initial data are close to the initial profile of the stationary one‐soliton, we obtain results on the asymptotic stability of the stationary one‐soliton under any small perturbation in [Formula: see text]. …”
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