Nondegenerate N-soliton solutions for Manakov system

Cai, Yue-Jin; Wu, Jian-Wen; Lin, Ji

doi:10.1016/j.chaos.2022.112657

Cited by 8 publications

(5 citation statements)

References 33 publications

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“…The MLVS approach can be considered as a nonlinear extension of the variable separation approach in linear equations. We hope that the MLVS approach may be used for other multi-dimensional integrable (and/or even non-integrable) NLEEs [27][28][29]. The more about the physical properties of multi-dimensional coherent structures obtained by the MLVS approach is worthy of studying further.…”

Section: Summary and Discussionmentioning

confidence: 98%

New interaction solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov-type system and fusion phenomena

Wang,

Lin,

Shen

2024

Commun. Theor. Phys.

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By means of the multilinear variable separation(MLVS) approach, new interaction solutions with low-dimensional arbitrary functions of the (2+1)-dimensional NNV-type system are constructed. Four-dromion structure, ring-parabolic soliton structure and corresponding fusion phenomena for the physical quantity U=ln f_{xy} are revealed for the first time. This MLVS approach can also be used to deal with the (2+1)-dimensional Sasa-Satsuma system.

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Section: Summary and Discussionmentioning

confidence: 98%

New interaction solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov-type system and fusion phenomena

Wang,

Lin,

Shen

2024

Commun. Theor. Phys.

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“…Concretely, we have demonstrated how to design the poses and the propagation velocities of nondegenerate solitons by choosing different diffraction coefficients, nonlinear effects and wave numbers, and also analyzed the dynamic behaviors of these nondegenerate solitons based on the analytical expressions (14) with Eqs. ( 11)-( 13), and expressions (16) with Eqs. ( 17) and (18).…”

Section: Discussionmentioning

confidence: 99%

“…Later, inspired by nondegenerate solitons, more general nondegenerate Kuznetsov-Ma breathers [12] and nondegenerate Akhmediev breathers [13,14] have also been studied. In recent years, based on several different mathematical physics methods such as the Hirota bilinear method, Kadomtsev-Petviashvili hierarchy reduction and developing Darboux transformation method, nondegenerate solitons have been reported in various multi-mode fiber systems, such as the Manakov systems, [15][16][17] generalized coupled nonlinear Schrödinger systems, [18][19][20][21][22] long-wave shortwave resonant interaction systems, [23] and coupled Fokas-Lenells systems. [24] Generally speaking, to describe the propagation of beams in two polarized directions, coupled nonlinear Schrödinger (CNLS) equations [25] iu z + 1 2 u tt + (|u| 2 + |v| 2 )u = 0, (1a)…”

Section: Introductionmentioning

confidence: 99%

Nondegenerate solitons of the (2+1)-dimensional coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optical fibers

Yang 杨,

Cheng 程,

Jin 金

et al. 2023

Chinese Phys. B

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In this work, we derive the multi-hump nondegenerate solitons for the (2+1)-dimensional coupled nonlinear Schrödinger (CNLS) equations with propagation distance dependent diffraction, nonlinearity and gain (loss) through the developing Hirota bilinear method and analyze the dynamical behaviors of these nondegenerate solitons. The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers, varying diffraction and nonlinearity parameters. In addition, when all the variable coefficients are chosen to be constants, the solutions obtained in this paper reduce to the shape-preserving nondegenerate solitons. Finally, it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.

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“…In the literature, there are many studies on models that include the term CD. Up to now, an extensive class of models regarding this matter in literature has been developed, such as Schrödinger-Hirota model [3,4], Radhakrishnan-Kundu-Lakshmanan model [5][6][7][8][9], Manakov system [10][11][12][13][14], Sasa-Satsuma model [15][16][17][18][19], Kundu-Eckhaus equation [20][21][22][23][24], and many more. Recently, some models have been derived by reckoning without the term chromatic dispersion and adding higher-order nonlinear terms from the literature.…”

Section: Introductionmentioning

confidence: 99%

Optical soliton solutions of the nonlinear Schrödinger equation in the presence of chromatic dispersion with cubic-quintic-septic-nonicnonlinearities

Ozdemir,

Secer,

Ozisik

et al. 2023

Phys. Scr.

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In this study, one of our main subjects is the examination of optical solitons of the nonlinear Schrödinger equation having cubic-quintic-septic-nonic nonlinearities via the modified F-expansion method. The other subject is also the analysis of the impacts of some parameters in the model on the soliton shape, which is examined for the first time in this study. According to the modified F-expansion method, we select the suitable transformation to gain the nonlinear ordinary differential equation for the nonlinear Schrödinger equation having cubic-quintic-septic-nonic nonlinearities in the first stage. Then, we get a system consisting of linear equations in polynomial form with the aid of the modified F-expansion method. Various solution sets consisting of the parameters of the nonlinear Schrödinger equation having cubic-quintic-septic-nonic nonlinearities are achieved. Inserting the selected sets and transformations into the serial form of the presented method and utilizing the solutions of the auxiliary equation in the presented method, the optical soliton solutions of the model are derived. Furthermore, varied optical soliton solutions, such as anti-kink, singular, and bright, are achieved, and 3D and 2D projections of the generated soliton solutions have been illustrated. The impact of some parameters on each soliton behavior has also been examined. It is found that these parameters have a significant impact on the soliton structure.

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Nondegenerate N-soliton solutions for Manakov system

Cited by 8 publications

References 33 publications

New interaction solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov-type system and fusion phenomena

New interaction solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov-type system and fusion phenomena

Nondegenerate solitons of the (2+1)-dimensional coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optical fibers

Optical soliton solutions of the nonlinear Schrödinger equation in the presence of chromatic dispersion with cubic-quintic-septic-nonicnonlinearities

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