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Embedded Solitons and Conservation Law with χ^{(2)} and χ^{(3)} Nonlinear Susceptibilities

100%
Savescu M., Kara A., Kumar S., Krishnan E., Zaka Ullah M., Moshokoa S., Zhou Q., Biswas A.
Acta Physica Polonica A
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2017
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vol. 131
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issue 2
297-303
EN
This paper studies embedded solitons that are confined to continuous spectrum, with χ^{(2)} and χ^{(3)} nonlinear susceptibilities. Bright and singular soliton solutions are obtained by the method of undetermined coefficients. Subsequently, the Lie symmetry analysis and mapping method retrieves additional solutions to the model such as shock waves, singular solitons, cnoidal waves, and several others. Finally, a conservation law for this model is secured through the Lie symmetry analysis.
2
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Optical Soliton Perturbation in Nonlinear Directional Couplers

100%
Vega-Guzman J., Babatin M., Biswas A.
|
EN
This paper secures soliton solutions to optical couplers in presence of Hamiltonian perturbation terms by the aid of undetermined coefficients. Both twin core couplers and multiple core couplers are studied. Bright, dark and singular soliton solutions are obtained for the model. The existence criteria for the solitons are also presented. The study is focused to the Kerr and power laws of nonlinearity.
3
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An eighth-order KdV-type equation in (1+1) and (2+1) dimensions: multiple soliton solutions

100%
Wazwaz A.-M.
Open Physics
|
2013
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vol. 11
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issue 1
143-146
EN
In this work we study an eighth-order KdV-type equations in (1+1) and (2+1) dimensions. The new equations are derived from the KdV6 hierarchy. We show that these equations give multiple soliton solutions the same as the multiple soliton solutions of the KdV6 hierarchy except for the dispersion relations.
4
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The collisions of two ion acoustic solitary waves in a magnetized nonextensive plasma

88%
El-Shamy E., Tribeche M., El-Taibany W.
Open Physics
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2014
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vol. 12
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issue 11
805-812
EN
Using the extended Poincaré-Lighthill-Kuo (EPLK) method, the interaction between two ion acoustic solitary waves (IASWs) in a multicomponent magnetized plasma (including Tsallis nonextensive electrons) has been theoretically investigated. The analytical phase shifts of the two solitary waves after interaction are estimated. The proposed model leads to rarefactive solitons only. The effects of colliding angle, ratio of number densities of (positive/negative) ions species to the density of nonextensive electrons, ion-to-electron temperature ratio, mass ratio of the negative-to-positive ions and the electron nonextensive parameter on the phase shifts are investigated numerically. The present results show that these parameters have strong effects on the phase shifts and trajectories of the two IASWs after collision. Evidently, this model is helpful for interpreting the propagation and the oblique collision of IASWs in magnetized multicomponent plasma experiments and space observations.
5
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Collision of water wave solitons

88%
Fenyvesi N., Bene G.
Open Physics
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2013
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vol. 11
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issue 11
1605-1615
EN
A classification of the time evolution of the two-soliton solutions of the Boussinesq equation is given, based on the number of extrema of the wave. For solitons moving in the same directions, three different scenarios are found, while it is shown that only one of these scenarios exists in case of oppositely moving solitons.
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