Various Dynamical Management of Three Solitons Through Modulated Coefficients in a Real Lossy Fiber System

Subramanian, K.; Hakkim, J.; Natarajan, V.; Bhuvaneshwari, B.; Indumathi, P.

doi:10.1007/s40819-022-01477-0

“…Inverse scattering transform method [1], Darboux transformation [2,3], Lie symmetry method [4], Bäcklund transformation [5], variable separation approach [6], Truncated Painlevé Approach and Hirota bilinear method [7] are just a few of the approaches that researchers are carrying out continuously on developing to resolve nonlinear evolution equations. It is possible to build localized coherent structures from the solution, including solitons [8,9], dromions [10], rogue waves [11], lumps [12] and breathers [13]. It is possible to perform an investigation of the collisional dynamics that are associated with the wave pattern.…”

Section: Introductionmentioning

confidence: 99%

Plenteous stationary wave patterns for (2+1) dimensional fokas system

Thilakavathy,

Amrutha,

Subramanian

et al. 2023

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This paper investigates the most straightforward extension of the (2+1) dimensional Nonlinear Schrödinger (NLS) equation, termed the Fokas system. The evolution equation is trilinearized, employing a unique method called Truncated Painlevé Approach (TPA) for the (2+1) dimensional Fokas System (FS). In terms of arbitrary functions, this method finds relatively extensive classes of solutions. Localized solutions, including dromion triplet, lump, multi-compacton and multi-rogue wave are generated by efficiently utilizing arbitrary functions. The analysis reveals that the localized solutions evolved do not move in space and only their amplitude changes with time.

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“…Inverse scattering transform method [1], Darboux transformation [2,3], Lie symmetry method [4], Bäcklund transformation [5], variable separation approach [6], Truncated Painlevé Approach and Hirota bilinear method [7] are just a few of the approaches that researchers are carrying out continuously on developing to resolve nonlinear evolution equations. It is possible to build localized coherent structures from the solution, including solitons [8,9], dromions [10], rogue waves [11], lumps [12] and breathers [13]. It is possible to perform an investigation of the collisional dynamics that are associated with the wave pattern.…”

Section: Introductionmentioning

confidence: 99%

Non-collisional Behaviour of Novel Nonlinear Wave Patterns for (2+1) Dimensional Fokas System

Thilakavathy

¹

,

Amrutha²,

Sivatharani

³

et al. 2023

Preprint

0

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This paper investigates the most straightforward extension of the (2+1) dimensional NLS equation, termed the Fokas system. The evolution equation is trilinearized, employing a unique method called Truncated Painlev\'{e} Approach for the (2+1) dimensional Fokas system. In terms of arbitrary functions, this method finds relatively extensive classes of solutions. Localized solutions, including dromion triplet, lump, multi-compacton and multi-rogue wave are generated by efficiently utilizing arbitrary functions. The analysis reveals that the localized solutions evolved do not move in space and only their amplitude changes with time.

show abstract