Controllable rogue wave and mixed interaction solutions for the coupled Ablowitz–Ladik equations with branched dispersion

2022 ◽  
Vol 123 ◽  
pp. 107591
Author(s):  
Xiao-Yong Wen ◽  
Cui-Lian Yuan
Keyword(s):  
Rogue Wave ◽  
Interaction Solutions

Localized interaction solution and its dynamics of the extended Hirota–Satsuma–Ito equation

2021 ◽  
pp. 2150313
Author(s):  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Chaudry Masood Khalique ◽  
Yong-Li Sun
Keyword(s):  
Numerical Simulations ◽  
Rogue Wave ◽  
The Other ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Physical Phenomena ◽  
Wave Phenomena ◽  
Hirota Bilinear ◽  
Ito Equation

In this research, we will introduce and study the localized interaction solutions and th eir dynamics of the extended Hirota–Satsuma–Ito equation (HSIe), which plays a key role in studying certain complex physical phenomena. By using the Hirota bilinear method, the lump-type solutions will be firstly constructed, which are almost rationally localized in all spatial directions. Then, three kinds of localized interaction solutions will be obtained, respectively. In order to study the dynamic behaviors, numerical simulations are performed. Two interesting physical phenomena are found: one is the fission and fusion phenomena happening during the procedure of their collisions; the other is the rogue wave phenomena triggered by the interaction between a lump-type wave and a soliton wave.

Localized waves and mixed interaction solutions with dynamical analysis to the Gross-Pitaevskii equation in the Bose-Einstein condensate

2021 ◽  
Author(s):  
Haotian Wang ◽  
Qin Zhou ◽  
Anjan Biswas ◽  
Wenjun Liu
Keyword(s):  
Rogue Wave ◽  
Rogue Waves ◽  
Transformation Method ◽  
Einstein Condensate ◽  
Dynamical Analysis ◽  
Pitaevskii Equation ◽  
Initial Profile ◽  
Interaction Solutions ◽  
Bose Einstein Condensate ◽  
Bose Einstein

Abstract We report a kind of breather, rogue wave and mixed interaction structures on a variational background height in the Gross-Pitaevskii equation in the Bose-Einstein condensate by the generalized Darboux transformation method, and the effects of related parameters on rogue wave structures are discussed. Numerical simulation can discuss the dynamics and stability of these solutions. We numerically confirm that these are correct, and can be reproduced from a deterministic initial profile. Results show that rogue waves and mixed interaction solutions can evolve with a small amplitude perturbation under the initial profile conditions, but breathers cannot. Therefore, these can be used to anticipate the feasibility of their experimental observation.

Interactions solutions of various-type rogue with multi-stripe solitons and breather lump for the (2+1)-dimensional Maccari’s system

2020 ◽  
Vol 34 (28) ◽  
pp. 2050268
Author(s):  
Jian-Wen Wu ◽  
Yue-Jun Deng ◽  
Ji Lin
Keyword(s):  
Rational Function ◽  
Exponential Function ◽  
Solitary Waves ◽  
Rogue Wave ◽  
Ansatz Method ◽  
Interaction Solutions

In this work, we consider the (2[Formula: see text]+[Formula: see text]1)-dimensional Maccari’s system, which is frequently introduced to describe the motion of the solitary waves. Abundant lump, line rogue wave, and dipole-type rogue wave are constructed by taking the ansatz method. Furthermore, the mixed interaction solutions between lump and multi-stripe solitons (such as fission and fusion) are obtained in combining rational function with exponential function. In particular, an interesting result is obtained: a rogue wave is excited from multi-stripe solitons.

Characteristics of Abundant Lumps and Interaction Solutions in the (4+1)-Dimensional Nonlinear Partial Differential Equation

2020 ◽  
Vol 21 (3-4) ◽  
pp. 283-289
Author(s):  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Rogue Wave ◽  
Nonlinear Partial Differential Equation ◽  
Soliton Solutions ◽  
Nonlinear Phenomena ◽  
Rational Solutions ◽  
Interaction Solutions ◽  
Rogue Wave Solution ◽  
Physics Model

AbstractIn this work, the (4+1)-dimensional Fokas equation, which is an important physics model, is under investigation. Based on the obtained soliton solutions, the new rational solutions are successfully constructed. Moreover, based on its bilinear formalism, a concise method is employed to explicitly construct its rogue-wave solution and interaction solution with an ansätz function. Finally, the main characteristics of these solutions are graphically discussed. Our results can be helpful for explaining some related nonlinear phenomena.

Interaction solutions to the (1+1)-dimensional generalized Drinfel’d–Sokolov–Wilson equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950329
Author(s):  
Shoufeng Shen ◽  
Xiaonan Ding ◽  
Rui Zhang ◽  
Xiaorui Hu
Keyword(s):  
Nonlinear Systems ◽  
Rogue Wave ◽  
Quadratic Function ◽  
Periodic Wave ◽  
Mathematical Software ◽  
Type Solution ◽  
Wave Type ◽  
Interaction Solutions ◽  
Type Interaction ◽  
Dynamical Features

In this paper, abundant interaction solutions for the (1[Formula: see text]+[Formula: see text]1)-dimensional generalized Drinfel’d–Sokolov–Wilson (gDSW) equation are presented. First, two groups of lump-soliton-type interaction solutions are constructed by using a combination of quadratic function and two exponential functions. Especially, lump-twin soliton-type solution therein can generate rogue wave, which rarely appears in (1[Formula: see text]+[Formula: see text]1)-dimensional nonlinear systems in comparison with (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear systems. When certain parameters are taken to zero, these exact solutions are reduced to corresponding lump, soliton and lumpoff solutions. Second, the lump-periodic wave-type and soliton-periodic wave-type interaction solutions are also found on the basis of the bilinear form of gDSW equation. In the concrete analysis, we use mathematical software Maple to deal with some complicated symbolic computations. Figures are presented to show the dynamical features of these solutions.

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

2020 ◽  
Vol 34 (07) ◽  
pp. 2050043 ◽  
Author(s):  
Feng-Hua Qi ◽  
Wen-Xiu Ma ◽  
Qi-Xing Qu ◽  
Pan Wang
Keyword(s):  
Rogue Wave ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Wave Solutions ◽  
Double Exponential ◽  
Dynamical Features ◽  
Wave Phenomena ◽  
Hirota Bilinear ◽  
Double Exponential Function ◽  
Dimensional Wave

By using the Hirota bilinear method, we construct new lump-type solutions to an extended [Formula: see text]-dimensional Jimbo–Miwa equation, which describes certain [Formula: see text]-dimensional wave phenomena in physics. The presented solutions contain 10 arbitrary parameters and only need to satisfy four restrictive conditions to be analytic, thereby enriching the existing lump-type solutions. Moreover, we compute their interaction solutions with double exponential function waves, which include rogue wave solutions. Dynamical features of the obtained solutions are graphically exhibited.

scholarly journals Lump and Mixed Rogue-Soliton Solutions of the (2 + 1)-Dimensional Mel’nikov System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Yue-jun Deng ◽  
Rui-yu Jia ◽  
Ji Lin
Keyword(s):  
Rational Function ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Bright Soliton ◽  
Half Line ◽  
Exponential Functions ◽  
Interaction Solutions ◽  
Mixed Solutions ◽  
Lump Wave ◽  
Interaction Phenomena

Lump wave and line rogue wave of the (2 + 1)-dimensional Mel’nikov system are derived by taking the ansatz as the rational function. By combining a rational function and different exponential functions, mixed solutions between the lump and soliton are derived. These solutions describe the interaction phenomena of the lump-bright soliton with fission and fusion, the half-line rogue wave with a bright soliton, and a rogue wave excited from the bright soliton pair, respectively. Some special concrete interaction solutions are depicted in both analytical and graphical ways.

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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