New Patterns of the Two-Dimensional Rogue Waves: (2+1)-Dimensional Maccari System*

Wang, Gaihua; Wang, Lihong; Rao, J. V.; He, Jingsong

doi:10.1088/0253-6102/67/6/601

Cited by 18 publications

(3 citation statements)

References 49 publications

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“…The propagation of soliton solution for various systems such as the modified inhomogeneous Hirota equation [20], inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system [21], Schrödinger Maxwell-Bloch equation [22] and Hirota-MB equation [23] are studied through the Darboux transformation method. The Exp-function approach [24], the generalized Riccati relation [25], the extended Fan sub-equation method [26], the bilinear method [27], reduction of the KP hierarchy [28], and closed-form solutions with arbitrary parameters have all been effectively found.…”

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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“…In recent years, notable advancements have been identified in the study of MS to generate solutions in the closed form. The Exp-function approach [45], the generalised Riccati relation [46], the extended Fan sub-equation method [47], the bilinear method [48], the extended modified auxiliary equation mapping method [49], and closed-form solutions with arbitrary parameters have all been effectively found.…”

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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“…Various exact solutions of local and nonlocal KP-type system (8) including solitons, breathers, rational, and semirational solutions have been reported [59][60][61][62][63][64] .…”

Section: Introductionmentioning

confidence: 99%

Rogue waves and lumps on the nonzero background in the ‐symmetric nonlocal Maccari system

Cao¹,

Cheng²,

Malomed

et al. 2021

Stud Appl Math

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In this paper, the scriptPT‐symmetric version of the Maccari system is introduced, which can be regarded as a two‐dimensional generalization of the defocusing nonlocal nonlinear Schrödinger equation. Various exact solutions of the nonlocal Maccari system are obtained by means of the Hirota bilinear method, long‐wave limit, and Kadomtsev–Petviashvili (KP) hierarchy method. Bilinear forms of the nonlocal Maccari system are derived for the first time. Simultaneously, a new nonlocal Davey‐Stewartson–type equation is derived. Solutions for breathers and breathers on top of periodic line waves are obtained through the bilinear form of the nonlocal Maccari system. Hyperbolic line rogue wave (RW) solutions and semirational ones, composed of hyperbolic line RW and periodic line waves are also derived in the long‐wave limit. The semirational solutions exhibit a unique dynamical behavior. Additionally, general line soliton solutions on constant background are generated by restricting different tau‐functions of the KP hierarchy, combined with the Hirota bilinear method. These solutions exhibit elastic collisions, some of which have never been reported before in nonlocal systems. Additionally, the semirational solutions, namely, (i) fusion of line solitons and lumps into line solitons and (ii) fission of line solitons into lumps and line solitons, are put forward in terms of the KP hierarchy. These novel semirational solutions reduce to 2N‐lump solutions of the nonlocal Maccari system with appropriate parameters. Finally, different characteristics of exact solutions for the nonlocal Maccari system are summarized. These new results enrich the structure of waves in nonlocal nonlinear systems, and help to understand new physical phenomena.

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New Patterns of the Two-Dimensional Rogue Waves: (2+1)-Dimensional Maccari System*

Cited by 18 publications

References 49 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

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

Rogue waves and lumps on the nonzero background in the ‐symmetric nonlocal Maccari system

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