On Nth-order rogue wave solution to nonlinear coupled dispersionless evolution equations

Zhaqilao, Zhaqilao

doi:10.1016/j.physleta.2012.09.050

Cited by 30 publications

(15 citation statements)

References 20 publications

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“…The general breather solution (20) satisfies the CGNLS equations with the conditions given in (16). The solution (20) given above, is periodic both in space and time directions as shown in Fig.1.…”

Section: Casementioning

confidence: 96%

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On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations

Priya

Senthilvelan

2015

Wave Motion

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We construct Darboux transformation of a coupled generalized nonlinear Schrödinger (CGNLS) equations and obtain exact analytic expressions of breather and rogue wave solutions. We also formulate the conditions for isolating these solutions. We show that the rogue wave solution can be found only when the four wave mixing parameter becomes real. We also investigate the modulation instability of the steady state solution of CGNLS system and demonstrate that it can occur only when the four wave mixing parameter becomes real. Our results give an evidence for the connection between the occurrence of rogue wave solution and the modulation instability.

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Section: Casementioning

confidence: 96%

“…The solution (20) given above, is periodic both in space and time directions as shown in Fig.1. We mention here that the components p and q are linearly dependent.…”

Section: Casementioning

confidence: 99%

On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations

Priya

Senthilvelan

2015

Wave Motion

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“…[29,30,31,32,33,34,35,36]. Motivated by this contemporary development, in this paper, we intend to construct the N-th order RW solution of this model.…”

Section: Introductionmentioning

confidence: 99%

Generalized Darboux transformation and Nth order rogue wave solution of a general coupled nonlinear Schrödinger equations

Priya

Senthilvelan

2015

Communications in Nonlinear Science and Numerical Simulation

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We construct a generalized Darboux transformation (GDT) of a general coupled nonlinear Schrödinger (GCNLS) system. Using GDT method we derive a recursive formula and present determinant representations for N-th order rogue wave solution of this system. Using these representations we derive first, second and third order rogue wave solutions with certain free parameters. By varying these free parameters we demonstrate the formation of triplet, triangle and hexagonal patterns of rogue waves.

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“…Very recently higher order RWs were also reported for certain nonlinear evolution equations, see for example Refs. [12][13][14][15][16]. It has been shown that these higher order RWs could reach higher peak amplitudes or exhibit multiple intensity peaks at different spatial locations and times.…”

Section: Introductionmentioning

confidence: 99%

Dark solitons, breathers, and rogue wave solutions of the coupled generalized nonlinear Schrödinger equations

2014

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We construct dark-dark soliton, general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of a coupled generalized nonlinear Schrödinger (CGNLS) equation. While dark-dark solitons are captured in the defocusing regime of the CGNLS system, the other solutions, namely, GB, AB, MS, and RW, are identified in the focusing regime. We also analyze the structures of GB, AB, MS, and RW profiles with respect to the four-wave mixing parameter. We show that when we increase the value of the real part of the four-wave mixing parameter, the number of peaks in the breather profile increases and the width of each peak shrinks. Interestingly, the direction of this profile also changes due to this change. As far as the RW profile is concerned the width of the peak becomes very thin when we increase the value of this parameter. Further, we consider the RW solution as the starting point, derive AB, MS, and GB in the reverse direction, and show that the solutions obtained in both directions match each other. In the course of the reverse analysis we also demonstrate how to capture the RW solutions directly from AB and MS.

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On Nth-order rogue wave solution to nonlinear coupled dispersionless evolution equations

Cited by 30 publications

References 20 publications

On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations

On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrödinger equations

Generalized Darboux transformation and Nth order rogue wave solution of a general coupled nonlinear Schrödinger equations

Dark solitons, breathers, and rogue wave solutions of the coupled generalized nonlinear Schrödinger equations

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