Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation

Rajan, M.S. Mani; Mahalingam, A.; Uthayakumar, A.

doi:10.1016/j.aop.2014.03.012

Cited by 61 publications

(11 citation statements)

References 35 publications

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“…This case represents more realistic models than those which are considered with constant coefficients . The soliton wave propagation in the above‐mode has been called “non‐autonomous soliton.” Hence, N‐soliton nonautonomous soliton interactions in various play a definitive role in the formation of the structure of wave and also the propagation direction with a phase shift in dispersive media …”

Section: Introductionmentioning

confidence: 99%

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On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Abdel‐Gawad

Tantawy

Yusuf

2019

Math Methods in App Sciences

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In this article, the generalized unified method (GUM) is used for finding multiwave solutions of the coupled Whitham‐Broer‐Kaup (WBK) equation with variable coefficients. Which describes the propagation of of shallow water waves. Here, we study the effects of the indirect nonlinear interaction of one‐, two‐ and three‐solitonic similaritons on the behavior of propagation of waves, in quasi‐periodic distributed system. This study can unable us to control the dynamics of type soliton (soliton, anti‐soliton) similaritons waves in dispersive waveguides. To give more physical insight to the obtained solutions, they are shown graphically. Their different structures are depicted by taking appropriate arbitrary functions. Further, with the suitable parameters, the indirect nonlinear interaction between two and three‐soliton waves are shown weal, in the sense that their amplitude does not blow up. Moreover, because of the importance of conservation laws Cls and stability analysis SA in the investigation of integrability, internal properties, existence, and uniqueness of a differential equation, we compute the Cls via multiplier technique and stability analysis via the concept of linear stability analysis for the WBK equations using the constant coefficients.

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Section: Introductionmentioning

confidence: 99%

“…Hence, N-soliton nonautonomous soliton interactions in various play a definitive role in the formation of the structure of wave and also the propagation direction with a phase shift in dispersive media. [18][19][20][21][22][23][24] The dispersive long (surface) water waves with time-dependent coefficient are given by the equations…”

Section: Introductionmentioning

confidence: 99%

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Abdel‐Gawad

Tantawy

Yusuf

2019

Math Methods in App Sciences

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“…Nonlinear tunneling has been discussed for the nonlinear Schrödinger equation [22][23][24][25]. Hereby, we will investigate the nonlinear tunneling for the KdV equation.…”

Section: Nonlinear Tunnelingmentioning

confidence: 99%

“…The concept of the nonlinear tunneling effect comes from the wave equations steming from the nonlinear dispersion relation, which has shown that the soliton can pass lossless through the barrier/well under special conditions which depend on the ratio between the amplitude of the soliton and the height of the barrier/well [22][23][24][25]. In this paper, we will apply such concept to Eq.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, nonlinear tunneling for the nonautonomous nonlinear Schrödinger equations has attracted attention in recent years [22][23][24][25]. The concept of the nonlinear tunneling effect comes from the wave equations steming from the nonlinear dispersion relation, which has shown that the soliton can pass lossless through the barrier/well under special conditions which depend on the ratio between the amplitude of the soliton and the height of the barrier/well [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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Spacial inhomogeneity and nonlinear tunneling for the forced KdV equation

Sun

Zhou

et al. 2018

Applied Mathematics Letters

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A variable-coefficient forced Korteweg-de Vries equation with spacial inhomogeneity is investigated in this paper. Under constraints, this equation is transformed into its bilinear form, and multi-soliton solutions are derived. Effects of spacial inhomogeneity for soliton velocity, width and background are discussed. Nonlinear tunneling for this equation is presented, where the soliton amplitude can be amplified or compressed. Our results might be useful for the relevant problems in fluids and plasmas.

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Numerous Exact Two-Pick, M-Shaped, and W-Shaped Solutions of Wavelength-Division-Multiplexed Channels of Optical Fibre Transmission Systems Described by Coupled Nonlinear Schrödinger Equations

Das,

Mondal

2024

Int J Theor Phys

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Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation

Cited by 61 publications

References 35 publications

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Spacial inhomogeneity and nonlinear tunneling for the forced KdV equation

Numerous Exact Two-Pick, M-Shaped, and W-Shaped Solutions of Wavelength-Division-Multiplexed Channels of Optical Fibre Transmission Systems Described by Coupled Nonlinear Schrödinger Equations

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