Dynamics of rogue waves in the Davey–Stewartson II equation

Ohta, Yuichi; Yang, Jianke

doi:10.1088/1751-8113/46/10/105202

Cited by 218 publications

(183 citation statements)

References 33 publications

(67 reference statements)

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“…Naturally, the higher order RW solutions have more peaks and exhibit several interesting patterns [39][40][41][42][43][44]. In addition to the NLS equation, there are many other equations admitting RW (or Peregrine-type) solutions such as the modified Korteweg-de Vries equation, the Fokas-Lenells equation, the derivative NLS equation, the long-wave-short-wave resonance equation, the vector NLS, the Davey-Stewartson equation and the KP-I equation [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59], etc.…”

Section: Indiamentioning

confidence: 99%

The Darboux transformation of the Kundu–Eckhaus equation

Qiu

Zhang³

et al. 2015

Proc. R. Soc. A.

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We construct an analytical and explicit representation of the Darboux transformation (DT) for the KunduEckhaus (KE) equation. Such solution and n-fold DT T n are given in terms of determinants whose entries are expressed by the initial eigenfunctions and 'seed' solutions. Furthermore, the formulae for the higher order rogue wave (RW) solutions of the KE equation are also obtained by using the Taylor expansion with the use of degenerate eigenvalues. ., all these parameters will be defined latter. These solutions have a parameter β, which denotes the strength of the non-Kerr (quintic) nonlinear and the self-frequency shift effects. We apply the contour line method to obtain analytical formulae of the length and width for the first-order RW solution of the KE equation, and then use it to study the impact of the β on the RW solution. We observe two interesting results on localization characters of β, such that if β is increasing from a/2: (i) the length of the RW solution is increasing as well, but the width is decreasing; (ii) there exist a significant rotation of the RW along the clockwise direction. We also observe the oppositely varying trend if β is increasing to a/2. We define an area of the RW solution and find that this area associated with c = 1 is invariant when a and β are changing.

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Section: Indiamentioning

confidence: 99%

The Darboux transformation of the Kundu–Eckhaus equation

Qiu

Zhang³

et al. 2015

Proc. R. Soc. A.

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“…Substituting the above seed solution into the Lax pair equations (17) and solving the resultant system of equations we obtain the following special solution with λ 1 = ih, namely…”

Section: First Order Rw Solutionmentioning

confidence: 99%

“…Certain kinds of exact solutions of NLS equation have been considered to describe possible mechanism for the formation of RWs such as Peregrine soliton [9], time periodic breather or Ma soliton (MS) [10,11] and space periodic breather or Akhmediev breather (AB) [12]. Subsequently attempts have been made to construct RW solutions through different methods for the NLS equation and its variants [13,14,15,16,17,18,19,20,21,22,23,24]. In this paper, we construct the N-th order RW solution of a general two coupled nonlinear Schrödinger (GCNLS) system [25],…”

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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“…Most recently, this method is used to obtain the N-dark soliton [15] and bright-dark mixed N-soliton [16] solutions of the multi-component Yajima-Oikawa (YO) system. In some other recent works, the KP hierarchy reduction technique has also been applied to derive rogue wave solutions of integrable systems [34][35][36], see also the literatures [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Bright-Dark Mixed N -Soliton Solution of Two-Dimensional Multicomponent Maccari System

Han

Chen

2017

Zeitschrift Für Naturforschung A

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By virtue of the KP hierarchy reduction technique, we construct the general bright-dark mixed N-soliton solution to the multi-component Mel'nikov system comprised of multiple (say M) short-wave components and one longwave component with all possible combinations of nonlinearities including all-positive, all-negative and mixed types. Firstly, the two-bright-one-dark (2-b-1-d) and one-bright-two-dark (1-b-2-d) mixed N-soliton solutions in short-wave components of the three-component Mel'nikov system are derived in detail. Then we extend our analysis to the M-component Mel'nikov system to obtain its general mixed N-soliton solution. The formula obtained unifies the allbright, all-dark and bright-dark mixed N-soliton solutions. For the collision of two solitons, the asymptotic analysis shows that for a M-component Mel'nikov system with M ≥ 3, inelastic collision takes place, resulting in energy exchange among the short-wave components supporting bright solitons only if the bright solitons appear at least in two short-wave components. Whereas, the dark solitons in the short-wave components and the bright solitons in the long-wave component always undergo elastic collision which just accompanied by a position shift.

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Dynamics of rogue waves in the Davey–Stewartson II equation

Cited by 218 publications

References 33 publications

The Darboux transformation of the Kundu–Eckhaus equation

The Darboux transformation of the Kundu–Eckhaus equation

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

Bright-Dark Mixed N -Soliton Solution of Two-Dimensional Multicomponent Maccari System

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