Different wave patterns for (2 + 1) dimensional Maccari’s equation

Thilakavathy, J.; Amrutha, R.; Subramanian, K.; Rajan, M.S. Mani

doi:10.1007/s11071-021-07179-4

Cited by 15 publications

(7 citation statements)

References 34 publications

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“…With the selection of the arbitrary functions φ 1 (x, y − t) and φ 2 (y) given in Eq. (38) and Eq. ( 39),the RWs can be generated.…”

Section: Rogue Wave Solutionmentioning

confidence: 99%

“…In this paper, one of the influential methods Truncated Painlevé Approach (TPA) [37][38][39][40] is utilised to obtain solution of (2+1) dimensional coupled integrable Maccari's System (MS) [41,42]. MS is a type of Nonlinear Evolution Equation (NLEE) widely used in nonlinear fields to describe the motion of isolated waves localized in a small area of space.…”

Section: Introductionmentioning

confidence: 99%

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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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“…With the selection of the arbitrary functions φ 1 (x, y − t) and φ 2 (y) given in Eq. (38) and Eq. ( 39),the RWs can be generated.…”

Section: Rogue Wave Solutionmentioning

confidence: 99%

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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show abstract

“…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.

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“…There are widespread concern about the existence of wave-like solutions in the ocean. At present, wave-like solutions have been mentioned by a large number of nonlinear systems, such as the Fokas-Lenells equation, [10] the (2 + 1)dimensional Maccari's system, [12] the nonlinear Schrödinger equation, [13] and the (3 + 1)-dimensional variable-coefficient nonlinear wave equation. [14] There are many ways to get wave-like solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Thilakavathy et al obtained the local solutions, such as multi-rogue wave solutions, rogue wave doublet solutions, and lump wave solutions by using TPA. [12] Ahmed et al constructed the additional solutions to the Maccari system by Lie symmetry approach. [15] Jabbari et al constructed exact solutions of the coupled Higgs equation and the Maccari system by the semi-inverse method and (G /G)expansion method.…”

Section: Introductionmentioning

confidence: 99%

Different wave patterns for two-coupled Maccari’s system with complex structure via truncated Painlevé approach

Ma 马,

Qi 戚,

Deng 邓

2023

Chinese Phys. B

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In this paper, we focused on the two-coupled Maccari’s system. With the help of Truncated Painlevé Approach(TPA), we express that local solution in the form of arbitrary functions. From the solution obtained, using its appropriate arbitrary functions, we have generated the rogue wave pattern solutions, rogue wave solutions and lump solutions. In addition, by controlling the values of the parameters in the solutions, we show the dynamic behaviors of the rogue wave pattern solutions, rogue wave solutions and lump solutions with the aid of Maple tool. The results of this study will contribute to the understanding of nonlinear wave dynamics in higher dimensional Maccari’s systems.

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Different wave patterns for (2 + 1) dimensional Maccari’s equation

Cited by 15 publications

References 34 publications

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

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

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

Different wave patterns for two-coupled Maccari’s system with complex structure via truncated Painlevé approach

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