Localized waves and interaction solutions to an extended (3+1)-dimensional Jimbo–Miwa equation

2019 ◽  
Vol 89 ◽  
pp. 70-77 ◽  
Author(s):  
Yunfei Yue ◽  
Lili Huang ◽  
Yong Chen
Keyword(s):  
Interaction Solutions ◽  
Localized Waves

N-lump and interaction solutions of localized waves to the (2+1)-dimensional generalized KDKK equation

2021 ◽  
pp. 104312
Author(s):  
Xuejun Zhou ◽  
Onur Alp Ilhan ◽  
Jalil Manafian ◽  
Gurpreet Singh ◽  
Nalbiy Salikhovich Tuguz
Keyword(s):  
Interaction Solutions ◽  
Localized Waves

Y-shaped soliton solutions for the (2+1)-dimensional bidirectional Sawada–Kotera equation

2021 ◽  
Author(s):  
Shuxin Yang ◽  
Zhao Zhang ◽  
Biao Li
Keyword(s):  
Soliton Solutions ◽  
Complex Interaction ◽  
High Order ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Dynamic Behaviors ◽  
Interaction Solutions ◽  
Localized Waves ◽  
Hirota Bilinear ◽  
Interaction Phenomenon

On the basis of the Hirota bilinear method, resonance Y-shaped soliton and its interaction with other localized waves of (2+1)-dimensional bidirectional Sawada–Kotera equation are derived by introducing the constraint conditions. These types of mixed soliton solutions exhibit complex interaction phenomenon between the resonance Y-shaped solitons and line waves, breather waves, and high-order lump waves. The dynamic behaviors of the interaction solutions are analyzed and illustrated.

Localized waves and interaction solutions to an extended (3+1)-dimensional Kadomtsev–Petviashvili equation

2020 ◽  
Vol 34 (06) ◽  
pp. 2050076 ◽  
Author(s):  
Han-Dong Guo ◽  
Tie-Cheng Xia ◽  
Wen-Xiu Ma
Keyword(s):  
Three Dimensional ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Dark Soliton ◽  
Complex Conjugate ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Parameter Constraints ◽  
Localized Waves

In this paper, an extended (3[Formula: see text]+[Formula: see text]1)-dimensional Kadomtsev–Petviashvili (KP) equation is studied via the Hirota bilinear derivative method. Soliton, breather, lump and rogue waves, which are four types of localized waves, are obtained. N-soliton solution is derived by employing bilinear method. Then, line or general breathers, two-order line or general breathers, interaction solutions between soliton and line or general breathers are constructed by complex conjugate approach. These breathers own different dynamic behaviors in different planes. Taking the long wave limit method on the multi-soliton solutions under special parameter constraints, lumps, two- and three-lump and interaction solutions between dark soliton and dark lump are constructed, respectively. Finally, dark rogue waves, dark two-order rogue waves and related interaction solutions between dark soliton and dark rogue waves or dark lump are also demonstrated. Moreover, dynamical characteristics of these localized waves and interaction solutions are further vividly demonstrated through lots of three-dimensional graphs.

Nonlinear localized waves resonance and interaction solutions of the (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

2020 ◽  
Vol 100 (2) ◽  
pp. 1527-1541 ◽  
Author(s):  
Juanjuan Wu ◽  
Yaqing Liu ◽  
Linhua Piao ◽  
Jianhong Zhuang ◽  
Deng-Shan Wang
Keyword(s):  
Interaction Solutions ◽  
Localized Waves

scholarly journals Novel Localized Waves and their Interaction Solutions for a Dimensionally Reduced (2+1)-dimensional Boussinesq Equation from N-soliton Solutions

2021 ◽  
Author(s):  
Dipankar Kumar ◽  
Md. Nuruzzaman ◽  
Gour Chandra Paul ◽  
Ashabul Hoque
Keyword(s):  
Water Waves ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Rogue Waves ◽  
Ocean Engineering ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Wave Limit ◽  
Localized Waves

Abstract The Boussinesq equation (BqE) has been of considerable interest in coastal and ocean engineering models for simulating surface water waves in shallow seas and harbors, tsunami wave propagation, wave over-topping, inundation, and near-shore wave process in which nonlinearity and dispersion effects are taken into consideration. The study deals with the dynamics of localized waves and their interaction solutions to a dimensionally reduced (2 + 1)-dimensional BqE from N-soliton solutions with the use of Hirota’s bilinear method (HBM). Taking the long-wave limit approach in coordination with some constraint parameters in the N-soliton solutions, the localized waves (i.e., soliton, breather, lump, and rogue waves) and their interaction solutions are constructed. The interaction solutions can be obtained among localized waves, such as (i) one breather or one lump from the two solitons, (ii) one stripe and one breather, and one stripe and one lump from the three solitons, and (iii) two stripes and one breather, one lump and one periodic breather, two stripes and one lump, two breathers, and two lumps from the four solitons. It is to be found that all interactions among the solitons are elastic. The energy, phase shift, shape, and propagation direction of these localized waves and their interaction solutions can be influenced and controlled by the involved constraint parameters. The dynamical characteristics of these localized waves and their interaction solutions are demonstrated through some 3D and density graphs. The outcomes achieved in this study can be used to illustrate the wave interaction phenomena in shallow water.

Dynamics of localized waves in a (3+1)-dimensional nonlinear evolution equation

2019 ◽  
Vol 33 (09) ◽  
pp. 1950101 ◽  
Author(s):  
Yunfei Yue ◽  
Yong Chen
Keyword(s):  
Evolution Equation ◽  
Soliton Solution ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Dark Soliton ◽  
Interaction Solutions ◽  
Localized Waves

In this paper, a (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear evolution equation is studied via the Hirota method. Soliton, lump, breather and rogue wave, as four types of localized waves, are derived. The obtained N-soliton solutions are dark solitons with some constrained parameters. General breathers, line breathers, two-order breathers, interaction solutions between the dark soliton and general breather or line breather are constructed by choosing suitable parameters on the soliton solution. By the long wave limit method on the soliton solution, some new lump and rogue wave solutions are obtained. In particular, dark lumps, interaction solutions between dark soliton and dark lump, two dark lumps are exhibited. In addition, three types of solutions related with rogue waves are also exhibited including line rogue wave, two-order line rogue waves, interaction solutions between dark soliton and dark lump or line rogue wave.

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