Painlevé integrability and multi-wave pattern for (2+1)-dimensional long wave–short wave resonance interaction system

Sivatharani, B; Subramanian, K.; Sekar, A.; Sundaram, P. V.

doi:10.1007/s11071-022-07523-2

Cited by 11 publications

(6 citation statements)

References 51 publications

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“…Earlier, TPA has been utilized to solve the (2+1) dimensional LSRI equations [29], NNV equation [30], AKNS equation [31], etc. The following are the processes involved in using TPA to solve the (2+1) dimensional CIMS: In terms of the non-characteristic singular manifold, the CIMS must be transformed into a multilinear equation.…”

Section: Introductionmentioning

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: Introductionmentioning

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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“…To the best of our knowledge, dromion triplet, multi-compacton and multi-rogue wave solutions have not been reported for the (2+1) dimensional Fokas system. Earlier, TPA has been utilized to solve the (2+1) dimensional AKNS equation [21], LSRI equations [22], NNV equation [23], Maccari equation [24,25] etc. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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

Thilakavathy,

Amrutha,

Subramanian

et al. 2023

Phys. Scr.

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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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“…Earlier, TPA has been utilized to solve the (2+1) dimensional AKNS equation [20], LSRI equations [21], NNV equation [22], Maccari equation [23,24] etc. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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

Thilakavathy

Amrutha²,

Sivatharani

et al. 2023

Preprint

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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

Painlevé integrability and multi-wave pattern for (2+1)-dimensional long wave–short wave resonance interaction system

Cited by 11 publications

References 51 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

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

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

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