Impact of fifth order dispersion on soliton solution for higher order NLS equation with variable coefficients

Vithya, Angelin; Rajan, M.S. Mani

doi:10.1016/j.joes.2019.11.002

Cited by 30 publications

(4 citation statements)

References 44 publications

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“…Localized solutions of (2+1) dimensional coupled integrable Maccari's system 3.1. Dromion solution Dromion is one of the nonlinear wave pattern [33,34] which originate at the intersection of two line solitons [35,36]. Unlike lumps [37][38][39] which decay algebraically, the tails of these waves decay exponentially in all directions.…”

Section: Solution Of (2+1) Dimensional Coupled Integrable Maccari's S...mentioning

confidence: 99%

A class of nonlinear wave patterns for (2+1) dimensional coupled integrable Maccari’s system

Sivatharani

Subramanian²,

Rajan³

et al. 2023

Phys. Scr.

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In this paper, with the aid of Truncated Painlev´e Approach, (2+1) dimensional Coupled Integrable Maccari’s System is investigated. The obtained result contains some arbitrary functions which can be properly selected to study the significance of the mathematical problem. Various kinds of localized solutions such as dromion triplet pairs, dromions, and rogue waves are derived from the obtained solution by means of appropriate arbitrary functions. Using suitable initial parameters, arbitrary functions are chosen to investigate the collisional behavior of the dromion triplet pairs in the two-dimensional plane. We graphically illustrated the nonlinear wave structures with the aid of 3D plots. It is worth noting that these localized nonlinear waves are unstable under various situations.

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Section: Solution Of (2+1) Dimensional Coupled Integrable Maccari's S...mentioning

confidence: 99%

A class of nonlinear wave patterns for (2+1) dimensional coupled integrable Maccari’s system

Sivatharani

Subramanian²,

Rajan³

et al. 2023

Phys. Scr.

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“…In the second set, it is considered that one of the eigenvalues λ 1 = ± √ τ 1 is positive and the other two eigenvalues are complex conjugate, namely λ 2 = ± √ β + iγ and λ 3 = ± √ β − iγ , where τ 1 = 2β and β varies from 0 to 0.5. Now, substituting the resultant expressions coming out from (11) and considering three admissible pairs of eigenvalues given above in (4), we can set up the double-periodic wave pattern as background for the Hirota equation (1).…”

Section: Demonstration On Hirota Equationmentioning

confidence: 99%

“…The nonlinear Schrödinger (NLS) equation describes the wave phenomena in the ocean [1][2][3][4] and the propagation of optical pulse in optical fiber [5][6][7][8][9]. Considering the external factors such as depth of the sea, bottom friction and viscosity in the ocean and the femtosecond pulse propagation in fibers, several higher-order NLS equations have been introduced in the literature [10][11][12][13][14][15]. One such higher-order NLS equation is the Hirota equation.…”

Section: Introductionmentioning

confidence: 99%

Rogue waves on the double-periodic background in Hirota equation

2021

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We construct rogue wave solutions on the double-periodic background for the Hirota equation through onefold Darboux transformation formula. We consider two types of double-periodic solutions as seed solutions. We identify the squared eigenfunctions and eigenvalues that appear in the onefold Darboux transformation formula through an algebraic method with two eigenvalues. We then construct the desired solution in two steps. In the first step, we create double-periodic waves as the background. In the second step, we build rogue wave solution on the top of this double-periodic solution. We present the localized structures for two different values of the arbitrary parameter each one with two different sets of eigenvalues.

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“…Dromions [1][2][3][4][5] are localized solutions originate at the intersection of two line-solitons [6][7][8][9][10][11][12][13]. In contrast to lumps [14][15][16] that decay just algebraically, they feature exponentially decaying tails in all directions.…”

Section: Introductionmentioning

confidence: 99%

Collisional Dynamics of Dromion Triplet for (2+1) Dimensional Coupled Integrable Maccari’s System

Sivatharani

Subramanian

Alagesan

et al. 2022

Preprint

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Using the Truncated Painlevѐ Approach, this work investigates the (2+1) dimensional coupled integrable Maccari’s system. As a result, the solutions are constructed in terms of arbitrary functions. Utilizing the arbitrary functions present in the solution, a variety of localized solutions such as dromion triplet pairs, dromions and rogue waves are generated. The dromion pairs in the two dimensional plane were constructed and their collisional behaviors were explored by selecting the arbitrary functions with adequate initial parameters. In addition to the dromion triplet pairs, dromions and rogue wave solutions were also generated. It is observed that the dromions and rogue waves are unstable and stationary. Keywords: Dromion triplet pairs, Rogue wave, Truncated Painlevѐ Approach

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Impact of fifth order dispersion on soliton solution for higher order NLS equation with variable coefficients

Cited by 30 publications

References 44 publications

A class of nonlinear wave patterns for (2+1) dimensional coupled integrable Maccari’s system

A class of nonlinear wave patterns for (2+1) dimensional coupled integrable Maccari’s system

Rogue waves on the double-periodic background in Hirota equation

Collisional Dynamics of Dromion Triplet for (2+1) Dimensional Coupled Integrable Maccari’s System

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