Rogue waves in the multicomponent Mel’nikov system and multicomponent Schrödinger–Boussinesq system

Sun, Bingrong; Lian, Zhan

doi:10.1007/s12043-017-1512-y

Cited by 16 publications

(14 citation statements)

References 56 publications

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“…Thus, they have attracted a lot of attention in the physics and nonlinear waves communities in recent years. Analytical expressions of rogue waves have been derived in a large number of integrable nonlinear wave equations, such as the nonlinear Schrödinger (NLS) equation [19][20][21][22][23][24][25][26][27][28], the derivative NLS equation [29,30], the three-wave interaction equation [31], the Davey-Stewartson equations [32,33], and many others [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. Rogue waves have also been observed in water tanks [54,55] and optical fibers [56][57][58].…”

Section: Introductionmentioning

confidence: 99%

“…The technique we will use is the bilinear Kadomtsev-Petviashvili (KP) reduction method [62]. Although this technique has been applied to derive rogue waves in several other integrable equations before [26,32,33,42,[49][50][51]53], when it is applied to the Boussinesq equation, the previous choices of differential operators within this technique would cause considerable technical complications. Here, we propose a new judicious choice of those differential operators, which will drastically simplify the dimension reduction calculation as well as the analytical expressions of rogue wave solutions.…”

Section: Introductionmentioning

confidence: 99%

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General Rogue Waves in the Boussinesq Equation

Yang

2020

J. Phys. Soc. Jpn.

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We derive general rogue wave solutions of arbitrary orders in the Boussinesq equation by the bilinear Kadomtsev-Petviashvili (KP) reduction method. These rogue solutions are given as Gram determinants with 2N − 2 free irreducible real parameters, where N is the order of the rogue wave. Tuning these free parameters, rogue waves of various patterns are obtained, many of which have not been seen before. Compared to rogue waves in other integrable equations, a new feature of rogue waves in the Boussinesq equation is that the rogue wave of maximum amplitude at each order is generally asymmetric in space. On the technical aspect, our contribution to the bilinear KP-reduction method for rogue waves is a new judicious choice of differential operators in the procedure, which drastically simplifies the dimension reduction calculation as well as the analytical expressions of rogue wave solutions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

General Rogue Waves in the Boussinesq Equation

Yang

2020

J. Phys. Soc. Jpn.

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“…The stable and unstable parametric regimes of DAWs are organized by the sign of P and Q of Eq. (28) [14,15,16,17,18,19,20]. When P and Q have same sign (i.e., P/Q > 0), the evolution of the DAWs amplitude is modulationally unstable in presence of the external perturbations.…”

Section: Modulational Instability and Rogue Wavesmentioning

confidence: 99%

“…The plot of P/Q against k yields stable and unstable parametric regimes of the DAWs. The point, at which the transition of P/Q curve intersect with k-axis, is known as threshold or critical wave number k (= k c ) [18,19,20,21,22,23,24,25]. The governing equation for highly energetic DARWs in the modulationally unstable parametric regime (P/Q > 0) can be written as [26,27,28,29,30]…”

Section: Modulational Instability and Rogue Wavesmentioning

confidence: 99%

Dust-acoustic rogue waves in non-thermal plasmas

et al. 2020

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The nonlinear propagation of dust-acoustic (DA) waves (DAWs) and associated DA rogue waves (DARWs), which are governed by the nonlinear Schrödinger equation, is theoretically investigated in a four component plasma medium containing inertial warm negatively charged dust grains and inertialess non-thermal distributed electrons as well as iso-thermal positrons and ions. The modulationally stable and unstable parametric regimes of DAWs are numerically studied for the plasma parameters. Furthermore, the effects of temperature ratios of ion-to-electron and ion-to-positron, and the number density of ion and dust grains on the DARWs are investigated. It is observed that the physical parameters play a very crucial role in the formation of DARWs. These results may be useful in understanding the electrostatic excitations in dusty plasmas in space and laboratory situations.

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“…In the previous studies, high‐order rogue waves in the NLS equation have been discussed, which are also localized in both space and time and could exhibit higher main peaks in fundamental pattern. In addition to the NLS equation, families of nonlinear soliton equations have been verified possessing rogue wave solutions …”

Section: Introductionmentioning

confidence: 99%

Novel high‐order breathers and rogue waves in the Boussinesq equation via determinants

Liu

Wazwaz

2019

Math Methods in App Sciences

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By virtue of the bilinear method and the Kadomtsev–Petviashvili (KP) hierarchy reduction technique, wider classes of high‐order breather and semirational and rogue wave solutions to the Boussinesq equation are derived. These solutions are presented explicitly in terms of Gram determinants, whose matrix elements have simply algebraic expressions. The breather and rogue wave solutions are derived from two different types of tau functions of a bilinear equation in the single‐component KP hierarchy. By taking a long wave limit of high‐order breather solutions, a range of hybrid solutions consisting of solitons, breathers, and one fundamental rogue wave are generated. For the rational rogue waves, some typical patterns such as Peregrine‐type, triple, and sextuple rogue waves are put forward by modifying the input parameters. Besides, a new rogue wave pattern of third‐order rogue waves is found, which features a mixture of a triangular pattern of three fundamental rogue waves and a fundamental pattern of second‐order rogue wave. These results may help understand the protean rogue wave manifestations in areas ranging from water waves to fluid dynamics.

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Rogue waves in the multicomponent Mel’nikov system and multicomponent Schrödinger–Boussinesq system

Cited by 16 publications

References 56 publications

General Rogue Waves in the Boussinesq Equation

General Rogue Waves in the Boussinesq Equation

Dust-acoustic rogue waves in non-thermal plasmas

Novel high‐order breathers and rogue waves in the Boussinesq equation via determinants

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