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Deformation rogue wave to the (2+1)-dimensional KdV equation
Xiaoen Zhang,Yong Chen +1 more
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TLDR
In this paper, a bilinear method was used to obtain the exact solution of the (2+1)-dimensional Korteweg-de Vries (KdV) equation.Abstract:
Deformation rogue wave as exact solution of the (2+1)-dimensional Korteweg–de Vries (KdV) equation is obtained via the bilinear method. It is localized in both time and space and is derived by the interaction between lump soliton and a pair of resonance stripe solitons. In contrast to the general method to get the rogue wave, we mainly combine the positive quadratic function and the hyperbolic cosine function, and then the lump soliton can be evolved rogue wave. Under the small perturbation of parameter, rich dynamic phenomena are depicted both theoretically and graphically so as to understand the property of (2+1)-dimensional KdV equation deeply. In general terms, these deformations mainly have three types: two rogue waves, one rogue wave or no rogue wave.read more
Citations
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Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation
Runfa Zhang,Sudao Bilige +1 more
TL;DR: In this article, a new method named bilinear neural network is introduced, and the corresponding tensor formula is proposed to obtain the exact analytical solutions of nonlinear partial differential equations (PDEs).
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Lump and interaction solutions to the (2+1)-dimensional Burgers equation
TL;DR: By the interaction between lump solution and a pair of resonance stripe solitons, a rogue wave phenomenon is revealed and the result shows that the lump soliton will be drowned or swallowed by the stripe soliton.
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Breather and hybrid solutions for a generalized (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation for the water waves
TL;DR: In this paper, a generalized B-dimensional Kadomtsev-Petviashvili equation for the water waves is investigated, and two kinds of the hybrid solutions composed of the breathers, lumps, line rogue waves and kink solitons are given.
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Rogue wave and a pair of resonance stripe solitons to KP equation
TL;DR: It is observed that the rogue wave, possessing a peak wave profile, arises from one of the resonance stripe solitons, moves to the other, and then disappears, therefore, a rogue wave can be generated by the interaction between the lump soliton and the pair of resonance stripesolitons.
Journal ArticleDOI
Consistent Riccati expansion and rational solutions of the Drinfel’d–Sokolov–Wilson equation
Bo Ren,Ji Lin,Zhi-Mei Lou +2 more
TL;DR: The consistent Riccati expansion is used to the Drinfel’d–Sokolov–Wilson (DSW) equation and it is demonstrated that the DSW equation is the CRE solvability system.
References
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Optical rogue waves
TL;DR: This work reports the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation—a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input.
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Water waves, nonlinear Schrödinger equations and their solutions
TL;DR: In this article, a number of ases in which these equations reduce to a one dimensional nonlinear Schrodinger (NLS) equation are enumerated, and several analytical solutions of NLS equations are presented, with discussion of their implications for describing the propagation of water waves.
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Rogue wave observation in a water wave tank.
TL;DR: This work presents the first experimental results with observations of the Peregrine soliton in a water wave tank, and proposes a new approach to modeling deep water waves using the nonlinear Schrödinger equation.
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Matter rogue waves
TL;DR: In this article, the existence of rogue waves in Bose-Einstein condensates either loaded into a parabolic trap or embedded in an optical lattice was shown to be possible.
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Extreme waves that appear from nowhere: On the nature of rogue waves
TL;DR: In this article, a plane wave is modulated by relatively weak random waves, and it is shown that the peaks with highest amplitude of the resulting wave composition can be described in terms of exact solutions of the focusing nonlinear Schrrodinger equation in the form of the collision of Akhmediev breathers.