The present article deals with M‐soliton solution and N‐soliton solution of the (2 + 1)‐dimensional asymmetrical Nizhnik–Novikov–Veselov equation by virtue of Hirota bilinear operator method. The ...obtained solutions for solving the current equation represent some localized waves including soliton, breather, lump, and their interactions, which have been investigated by the approach of the long‐wave limit. Mainly, by choosing the specific parameter constraints in the M‐soliton and N‐soliton solutions, all cases of the one breather or one lump can be captured from the two, three, four, and five solitons. In addition, the performances of the mentioned technique, namely, the Hirota bilinear technique, are substantially powerful and absolutely reliable to search for new explicit solutions of nonlinear models. Meanwhile, the obtained solutions are extended with numerical simulation to analyze graphically, which results in localized waves and their interaction from the two‐, three‐, four‐, and five‐soliton solutions profiles. They will be extensively used to report many attractive physical phenomena in the fields of acoustics, heat transfer, fluid dynamics, classical mechanics, and so on.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
We consider coupled weakly birefringent cavities filled-in with nonlinear Kerr material and subject to linearly polarized optical injection. Light propagation in such a system is described by a ...system of discrete Lugiato–Lefever-type equations for each linear polarization component of the electric field into each cavity, coupled by the cross-phase modulation terms and the neighboring waveguides field overlap integrals. We demonstrate that this system supports stable three-dimensional vector localized structures often called discrete vector light bullets. We consider both anomalous and normal dispersion and show that it results in the generation of, respectively, bright and dark discrete vector light bullets. Due to the polarization multistability of the system, we demonstrated coexisting light bullets with polarization at the light bullets peaks as different as predominantly linear to predominantly circular. We have shown that chaotic spatio-temporal dynamics can be realized even for such an injection strengths for which the light bullets distribution in the system is stationary by increasing the coupling strength C between the cavities.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
3.
Three-dimensional hybrid vortex solitons Driben, Rodislav; Kartashov, Yaroslav V; Malomed, Boris A ...
New journal of physics,
06/2014, Volume:
16, Issue:
6
Journal Article, Publication
Peer reviewed
Open access
We show, by means of numerical and analytical methods, that media with a repulsive nonlinearity which grows from the center to the periphery support a remarkable variety of previously unknown complex ...stationary and dynamical three-dimensional (3D) solitary-wave states. Peanut-shaped modulation profiles give rise to vertically symmetric and antisymmetric vortex states, and novel stationary hybrid states, built of top and bottom vortices with opposite topological charges, as well as robust dynamical hybrids, which feature stable precession of a vortex on top of a zero-vorticity soliton. The analysis reveals stability regions for symmetric, antisymmetric, and hybrid states. In addition, bead-shaped modulation profiles give rise to the first example of exact analytical solutions for stable 3D vortex solitons. The predicted states may be realized in media with a controllable cubic nonlinearity, such as Bose-Einstein condensates.
The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as x\to\infty. He finds that the ...amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward y=\pm\infty. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.
Soliton resonances and soliton molecules have become a hot topic in the field of nonlinear science and engineering in recent years due to their potential applications. This work presents a systematic ...study of the soliton interaction dynamics of the Maccari system. Using the bilinear method, explicit first- and second-order solutions of the system are derived for the system. With these solutions and carefully chosen parameters, we observe various soliton interaction phenomena, such as soliton resonances, soliton molecules, soliton oscillations, and heterotypic solitons, including the V- and Y-type soliton, for the two dependent variables under two coordinate systems: space and spatiotemporal coordinate systems, respectively. Notably, we find that soliton molecules and heterotypic solitons exhibit completely different features under the two coordinate systems. The constraint conditions for the existence of soliton molecules are more restrictive in the spatiotemporal coordinate, and the occurrence of V- and Y-type soliton patterns is relatively rare in this coordinate system.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In nonlinear science, the interactions among solitons are well studied because the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study ...interactions among different types of nonlinear waves such as the solitons (or solitary waves), the cnoidal periodic waves and Painlevé waves. In this paper, taking the Kadomtsev–Petviashvili (KP) equation as an illustration model, a new method is established to find interactions among different types of nonlinear waves. The nonlocal symmetries related to the Darboux transformation (DT) of the KP equation is localized after embedding the original system to an enlarged one. Then the DT is used to find the corresponding group invariant solutions. It is shown that the essential and unique role of the DT is to add an additional soliton on a Boussinesq-type wave or a KdV-type wave, which are two basic reductions of the KP equation.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Nonlinear control is widely used in optical communications, ultrafast optics and other fields. In this paper, nonlinear control based on the dark soliton is investigated in the dispersion management ...system. Dark soliton solutions for the third-order nonlinear Schrödinger equation are derived. Through changing the group velocity dispersion and nonlinear parameters, the propagation characteristics of dark solitons are discussed, and the influences of corresponding parameters on dark solitons are analyzed. Some nonlinear control methods based on specific parameters are suggested. Results are beneficial to the study of the dark soliton transmission.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•Our paper reports the presence and stability characteristics of solitons within deformed photonic graphene featuring Kerr nonlinearity.•We identified that the band structure of photonic graphene ...comprises Dirac cones, significantly influenced by deformation.•Stable soliton solutions, including fundamental and out-of-dipole solitons, are observed within the semi-infinite gap of photonic graphene.•Conversely, in-phase two-peaked solitons, out-of-phase tripolar solitons, and quadruple solitons are inherently unstable.
We investigate the formation and evolution of two-dimensional solitons and vortices in deformed photonic graphene, encompassing fundamental solitons, multipole solitons, and vortex solitons. Using the plane-wave expansion method, we analyze the bandgap structure of photonic graphene, revealing Dirac cones whose characteristics are influenced by deformation. Soliton generation results from lattice potential deformation, linear energy gap modulation, and nonlinear effects. Specifically, fundamental and dipole solitons, exhibiting out-of-phase behavior, propagate robustly within photonic graphene, maintaining structural integrity over extended distances, while other soliton solutions are unstable. Furthermore, we explore the realization and propagation characteristics of vortex solitons with unit topological charge within photonic graphene.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In this paper, the analytic three-soliton solution for a high-order nonlinear Schrödinger equation is obtained by the Hirota’s bilinear method. The transmission characteristics of three solitons are ...discussed. By selecting relevant parameters, soliton interactions are presented, and the method of generating new solitons is suggested. The influences of corresponding parameters on soliton transmission and interactions are analyzed. Results of this paper are helpful for enriching the soliton theory and studying the signal routing system.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
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