On the evolution of a rogue wave along the orthogonal direction of the (t, x)-plane

Yuan, Feng; Qiu, Deqin; Liu, Wei; Porsezian, K.; He, Jingsong

doi:10.1016/j.cnsns.2016.08.012

Cited by 14 publications

(4 citation statements)

References 32 publications

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“…However, the reductions for bright and bright-dark solitons are different from the ones for dark solitons in the current paper. On the other hand, rogue waves, as a special phenomenon of solitary waves originally occurring in the deep ocean, have drawn more and more attentions in many other fields [43][44][45]. As mentioned in Section 1, the KP hierarchy reduction method can also be applied to derive lump and rogue wave solutions of soliton equations.…”

Section: Discussionmentioning

confidence: 99%

GeneralN-Dark Soliton Solutions of the Multi-Component Mel’nikov System

Han

Chen

2017

J. Phys. Soc. Jpn.

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A general form of N-dark soliton solutions of the multi-component Mel'nikov system is presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general N-dark-dark soliton solutions in Gram determinant form are constructed through the KP hierarchy reduction method. The dynamics of single dark-dark soliton and two dark-dark solitons are discussed in detail. It can be shown that the collisions of dark-dark solitons are elastic and energies of the solitons in different components completely transmit through. In addition, the dark-dark soliton bound states including both stationary and moving cases are also investigated. An interesting feature for the coupled Mel'nikov system is that the stationary darkdark soliton bound states can exist for all possible combinations of nonlinearity coefficients including all-positive, all-negative and mixed types, while the moving case are possible when they take opposite signs or they are both negative. The dynamics and several interesting structures of the solutions are illustrated through some figures.

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Section: Discussionmentioning

confidence: 99%

GeneralN-Dark Soliton Solutions of the Multi-Component Mel’nikov System

Han

Chen

2017

J. Phys. Soc. Jpn.

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“…[42]. Those results have also been extended to other NLS-type equation with additional derivative terms [43,44]. It is worthwhile and natural to know whether or not it has other solutions or interesting dynamics.…”

Section: Introductionmentioning

confidence: 72%

Generating mechanism and dynamic of the smooth positons for the derivative nonlinear Schrödinger equation

Song

et al. 2019

Nonlinear Dyn

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Based on the degenerate Darboux transformation, the n-order smooth positon solutions for the derivative nonlinear Schrödinger equation are generated by means of the general determinant expression of the N -soliton solution, and interesting dynamic behaviors of the smooth positons are shown by the corresponding three dimensional plots in this paper. Furthermore, the decomposition process, bent trajectory and the change of the phase shift for the positon solutions are discussed in detail. Additional, three kinds of mixed solutions, namely (1) the hybrid of one-positon and two-positon solutions, (2) the hybrid of two-positon and two-positon solutions, and (3) the hybrid of onesoliton and three-positon solutions are presented and their rather complicated dynamics are revealed.

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“…It is expressed by quadratic polynomials and features an 'amplitude peak' which is localized in space-time and has three times the background height; hence, it has been used to model rare rogue wave events. Thus far, a series of systematic methods used to generate higher-order rogue wave solutions of the NLS equation have been established [7][8][9][10][11][12][13][14][15][16][17][18]. However, in order to better control, manage and predict complicated rogue waves, one should not be satisfied with the simple scalar NLS framework.…”

Section: Introductionmentioning

confidence: 99%

Rogue waves in the three-level defocusing coupled Maxwell–Bloch equations

Wang

Wei

et al. 2021

Proc. R. Soc. A.

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The coupled Maxwell–Bloch (CMB) system is a fundamental model describing the propagation of ultrashort laser pulses in a resonant medium with coherent three-level atomic transitions. In this paper, we consider an integrable generalization of the CMB equations with the defocusing case. The CMB hierarchy is derived with the aid of a 3 × 3 matrix eigenvalue problem and the Lenard recursion equation, from which the defocusing CMB model is proposed as a special reduction of the general CMB equations. The n -fold Darboux transformation as well as the multiparametric n th-order rogue wave solution of the defocusing CMB equations are put forward in terms of Schur polynomials. As an application, the explicit rogue wave solutions from first to second order are presented. Apart from the traditional dark rogue wave, bright rogue wave and four-petalled rogue wave, some novel rogue wave structures such as the dark four-peaked rogue wave and the double-ridged rogue wave are found. Moreover, the second-order rogue wave triplets which contain a fixed number of these rogue waves are shown.

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On the evolution of a rogue wave along the orthogonal direction of the (t, x)-plane

Cited by 14 publications

References 32 publications

GeneralN-Dark Soliton Solutions of the Multi-Component Mel’nikov System

GeneralN-Dark Soliton Solutions of the Multi-Component Mel’nikov System

Generating mechanism and dynamic of the smooth positons for the derivative nonlinear Schrödinger equation

Rogue waves in the three-level defocusing coupled Maxwell–Bloch equations

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