Abundant optical solitons to the (2+1)-dimensional Kundu-Mukherjee-Naskar equation in fiber communication systems

Ghanbari, Behzad; Baleanu, Dumitru

doi:10.1007/s11082-023-05457-6

Cited by 20 publications

(2 citation statements)

References 63 publications

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“…It is increasingly important to find exact solutions for nonlinear evolution equations (NLEEs) because they illustrate new nonlinear phenomena that emerge in mathematical physics. Various scientific fields can use such equations to explain complex physical phenomena, especially in plasma physics, solid-state physics, ecology, and quantum mechanics [1][2][3][4][5][6][7]. The construction of exact solutions for NLEEs has created a very interesting and dynamic field whose historical background goes back to the discovery of soliton solutions in 1834 [8].…”

Section: Introductionmentioning

confidence: 99%

Multiple localized waves to the (2+1)-dimensional shallow water waveequation on non-flat constant backgrounds and their applications

Cao,

Tian,

Ghanbari

et al. 2024

Phys. Scr.

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In this paper, a new general bilinear Backlund transformation and Lax pair for the (2+1)-dimensional shallow water wave equation are given in terms of the binary Bell polynomials. Based on this transformation along with introducing an arbitrary function, the multi-kink soliton, line breather, and multi-line rogue wave solutions on a non-flat constant background plane are derived. Further, we foundthat the dynamic pattern of line breather on the background of periodic line waves are similar to the two-periodic wave solutions obtained through a multi-dimensional Riemann theta function. Also, the generation mechanism and smooth conditions of the line rogue waves on the periodic line wave background are presented with longwave limit method. Additionally, a family of new rational solutions, consisting of line rogue waves and line solitons, are derived, which have never been reported before. Furthermore, the present work can be directly applied to other nonlinear equations.

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Section: Introductionmentioning

confidence: 99%

Multiple localized waves to the (2+1)-dimensional shallow water waveequation on non-flat constant backgrounds and their applications

Cao,

Tian,

Ghanbari

et al. 2024

Phys. Scr.

Self Cite

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“…There are many techniques that are developed to gained the exact solitary wave solutions such as generalized exponential rational function method 28 – 32 , Hirota’s bilinear transform 33 , 34 , Jacobian elliptic functions method 35 , and etc. Ghanbari, B. used the generalized exponential rational function method and constructed the different form of optical soliton solutions for the Hirota-Maccari equation 36 and Kundu-Mukherjee-Naskar equation 37 , generalized Schamel equation [?].…”

Section: Introductionmentioning

confidence: 99%

Novel waves structures for the nonclassical Sobolev-type equation in unipolar semiconductor with its stability analysis

Shahzad,

Ahmed,

Baber

et al. 2023

Sci Rep

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In this study, the Sobolev-type equation is considered analytically to investigate the solitary wave solutions. The Sobolev-type equations are found in a broad range of fields, such as ecology, fluid dynamics, soil mechanics, and thermodynamics. There are two novel techniques used to explore the solitary wave structures namely as; generalized Riccati equation mapping and modified auxiliary equation (MAE) methods. The different types of abundant families of solutions in the form of dark soliton, bright soliton, solitary wave solutions, mixed singular soliton, mixed dark-bright soliton, periodic wave, and mixed periodic solutions. The linearized stability of the model has been investigated. Solitons behave differently in different circumstances, and their behaviour can be better understood by building unique physical problems with particular boundary conditions (BCs) and starting conditions (ICs) based on accurate soliton solutions. So, the choice of unique physical problems from various solutions is also carried out. The 3D, line graphs and corresponding contours are drawn with the help of the Mathematica software that explains the physical behavior of the state variable. This information can help the researchers in their understanding of the physical conditions.

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A variety of optical wave solutions to space–time fractional perturbed Kundu–Eckhaus model with full non-linearity

Zafar,

Raheel,

Tariq

et al. 2024

Opt Quant Electron

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In this paper, the new optical wave solutions of truncated M-fractional perturbed Kundu-Eckhaus model with full non-linearity are obtained by utilizing the exp a function technique and modified extended tanh expansion function technique. The solutions are in the form of dark soliton, bright soliton, singular solitons and other form of solutions. The gained solutions are helpful for the further development of concerned model. The obtained results have also been presented graphically in both two-dimensional and three-dimensional formats to discuss the dynamical features as well as the parametric dependence of the constructed solutions. The study offers a highly spectacular and acceptable techniques to combine various intriguing wave demonstrations for more sophisticated models of the modern day.

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Abundant optical solitons to the (2+1)-dimensional Kundu-Mukherjee-Naskar equation in fiber communication systems

Cited by 20 publications

References 63 publications

Multiple localized waves to the (2+1)-dimensional shallow water waveequation on non-flat constant backgrounds and their applications

Multiple localized waves to the (2+1)-dimensional shallow water waveequation on non-flat constant backgrounds and their applications

Novel waves structures for the nonclassical Sobolev-type equation in unipolar semiconductor with its stability analysis

A variety of optical wave solutions to space–time fractional perturbed Kundu–Eckhaus model with full non-linearity

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