scholarly journals Resonance Y-shape Solitons and Mixed Solutions for a (2+1)-dimensional Generalized Caudrey-Dodd-Gibbon-Kotera-Sawada Equation in Fluid Mechanics

2021 ◽  
Author(s):  
hongcai ma ◽  
Shupan Yue ◽  
Aiping Deng
Keyword(s):  
Fluid Mechanics ◽  
Soliton Solutions ◽  
Resonance Method ◽  
Bilinear Method ◽  
Specific Expression ◽  
Mixed Solutions ◽  
Before And After ◽  
Wave Limit ◽  
Trajectory Equation ◽  
Resonant Method

Abstract Under the well-known bilinear method of Hirota, the specific expression for N-soliton solutions of (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada(gCDGKS) equation in fluid mechanics is given. By defining a noval restrictive condition on N-soliton solutions, resonant Y-type and X-type soliton solutions are generated. Under the previous new constraints, combined with the velocity resonance method and module resonant method, the mixed solutions of resonant Y-type solitons and line waves, breather solutions are found. Finally, with the support of long wave limit method, the interaction between resonant Ytype solitons and higher-order lumps is shown, and the motion trajectory equation before and after the interaction between lumps and resonant Y-type solitons is derived.

Families of exact solutions of the generalized (3+1)-dimensional nonlinear-wave equation

2018 ◽  
Vol 32 (29) ◽  
pp. 1850359 ◽  
Author(s):  
Wenhao Liu ◽  
Yufeng Zhang
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Lump Solution ◽  
Rational Solutions ◽  
Bilinear Method ◽  
The One ◽  
Wave Limit

In this paper, the traveling wave method is employed to investigate the one-soliton solutions to two different types of bright solutions for the generalized (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear-wave equation, primarily. In the following parts, we derive the breathers and rational solutions by using the Hirota bilinear method and long-wave limit. More specifically, we discuss the lump solution and rogue wave solution, in which their trajectory will be changed by varying the corresponding coefficient or coordinate axis. On the one hand, the breathers express the form of periodic line waves in different planes, on the other hand, rogue waves are localized in time.

Soliton molecules and some novel hybrid solutions for (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

2021 ◽  
pp. 2150388
Author(s):  
Hongcai Ma ◽  
Huaiyu Huang ◽  
Aiping Deng
Keyword(s):  
Soliton Solutions ◽  
Dynamic Graphs ◽  
Bilinear Method ◽  
Resonance Mechanism ◽  
Long Wave ◽  
Petviashvili Equation ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Bkp Equation

In recent years, soliton molecules have received reinvigorating scientific interests in physics and other fields. Soliton molecules have been successfully found in optical experiments. In this paper, we attribute the solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by employing the bilinear method. Based on the [Formula: see text]-soliton solutions, we establish the soliton molecules, asymmetric solitons and some novel hybrid solutions of this equation by means of the velocity resonance mechanism and the long wave limit method. Finally, we give dynamic graphs of soliton molecules, asymmetric solitons and some novel hybrid solutions.

Diverse solitons and interaction solutions for the (2+1)-dimensional CDGKS equation

2019 ◽  
Vol 33 (16) ◽  
pp. 1950174 ◽  
Author(s):  
Jian-Hong Zhuang ◽  
Yaqing Liu ◽  
Xin Chen ◽  
Juan-Juan Wu ◽  
Xiao-Yong Wen
Keyword(s):  
Soliton Solutions ◽  
Propagation Direction ◽  
Soliton Interaction ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Long Wave ◽  
Wave Limit ◽  
Hirota Bilinear ◽  
Line Soliton

In this paper, the (2[Formula: see text]+[Formula: see text]1)-dimensional CDGKS equation is studied and its diverse soliton solutions consisting of line soliton, periodic soliton and lump soliton with different parameters are derived based on the Hirota bilinear method and long-wave limit method. Based on exact solution formulae with different parameters, the interaction between line soliton and periodic soliton, the interaction between line soliton and lump soliton, as well as the interaction between periodic soliton and lump soliton are illustrated. According to the dynamical behaviors, it can be found that the effects of different parameters are on the propagation direction and shapes. Novel soliton interaction phenomena are also observed.

High-order breathers, lumps and hybrid solutions to the (2+1)-dimensional fifth-order KdV equation

2019 ◽  
Vol 33 (22) ◽  
pp. 1950255 ◽  
Author(s):  
Wen-Tao Li ◽  
Zhao Zhang ◽  
Xiang-Yu Yang ◽  
Biao Li
Keyword(s):  
Kdv Equation ◽  
Perturbation Expansion ◽  
Soliton Solutions ◽  
High Order ◽  
Bilinear Method ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Fifth Order ◽  
Parameter Constraints

In this paper, the (2+1)-dimensional fifth-order KdV equation is analytically investigated. By using Hirota’s bilinear method combined with perturbation expansion, the high-order breather solutions of the fifth-order KdV equation are generated. Then, the high-order lump solutions are also derived from the soliton solutions by a long-wave limit method and some suitable parameter constraints. Furthermore, we extend this method to obtain hybrid solutions by taking long-wave limit for partial soliton solutions. Finally, the dynamic behavior of these solutions is presented in the figures.

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.

Multiple breathers and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

2021 ◽  
Author(s):  
Na Liu ◽  
Xinhua Tang ◽  
Weiwei Zhang
Keyword(s):  
Soliton Solutions ◽  
High Order ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Dynamical Characteristics ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Wave Limit ◽  
Hirota Bilinear ◽  
Bkp Equation

This paper is devoted to obtaining the multi-soliton solutions, high-order breather solutions and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by applying the Hirota bilinear method and the long-wave limit approach. Moreover, the interaction solutions are constructed by choosing appropriate value of parameters, which consist of four waves for lumps, breathers, rouges and solitons. Some dynamical characteristics for the obtained exact solutions are illustrated using figures.

Hybrid soliton solutions in the (2+1)-dimensional nonlinear Schrödinger equation

2017 ◽  
Vol 31 (32) ◽  
pp. 1750298 ◽  
Author(s):  
Meidan Chen ◽  
Biao Li
Keyword(s):  
Rogue Wave ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Nls Equation ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Long Wave ◽  
Hybrid Solutions ◽  
Wave Limit

Rational solutions and hybrid solutions from N-solitons are obtained by using the bilinear method and a long wave limit method. Line rogue waves and lumps in the (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger (NLS) equation are derived from two-solitons. Then from three-solitons, hybrid solutions between kink soliton with breathers, periodic line waves and lumps are derived. Interestingly, after the collision, the breathers are kept invariant, but the amplitudes of the periodic line waves and lumps change greatly. For the four-solitons, the solutions describe as breathers with breathers, line rogue waves or lumps. After the collision, breathers and lumps are kept invariant, but the line rogue wave has a great change.

Soliton turbulence in electronegative plasma due to head-on collision of multi solitons

2020 ◽  
Vol 75 (12) ◽  
pp. 999-1007
Author(s):  
Rustam Ali ◽  
Anjali Sharma ◽  
Prasanta Chatterjee
Keyword(s):  
Wave Field ◽  
Soliton Solutions ◽  
Negative Ions ◽  
First Integral ◽  
Statistical Properties ◽  
Charged Dust ◽  
Bilinear Method ◽  
Electronegative Plasma ◽  
Kdv Equations ◽  
First Four Moments

AbstractHead-on interaction of four dust ion acoustic (DIA) solitons and the statistical properties of the wave field due to head-on interaction of solitons moving in opposite direction is studied in the framework of two Korteweg de Vries (KdV) equations. The extended Poincaré–Lighthill–Kuo (PLK) method is applied to obtain two opposite moving KdV equations from an unmagnetized four component plasma model consisting of Maxwellian negative ions, cold mobile positive ions, κ-distributed electrons and positively charged dust grains. Hirota’s bilinear method is adopted to obtain two-soliton solutions of both the KdV equations and accordingly act of soliton turbulence is presented due to head-on collision of four solitons. The amplitude and shape of the resultant wave profile at the point of strongest interaction are obtained. To see the effect of head-on collision on the statistical properties of wave field the first four moments are computed. It is observed that the head-on collision has no effect on the first integral moment while the second, third and fourth moments increase in the dominant interaction region of four solitons, which is a clean indication of soliton turbulence.

Multiple Soliton Solutions for a Variety of Coupled Modified Korteweg–de Vries Equations

2011 ◽  
Vol 66 (10-11) ◽  
pp. 625-631
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Mkdv Equation ◽  
Resonance Phenomenon ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Multiple Soliton Solutions ◽  
De Vries ◽  
Coupled Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

We make use of Hirota’s bilinear method with computer symbolic computation to study a variety of coupled modified Korteweg-de Vries (mKdV) equations. Multiple soliton solutions and multiple singular soliton solutions are obtained for each coupled equation. The resonance phenomenon of each coupled mKdV equation is proved not to exist.

Lumps, breathers, rogue waves and interaction solutions to a (3+1)-dimensional Kudryashov–Sinelshchikov equation

2020 ◽  
Vol 34 (12) ◽  
pp. 2050117 ◽  
Author(s):  
Xianglong Tang ◽  
Yong Chen
Keyword(s):  
Rogue Waves ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Long Wave ◽  
Wave Limit ◽  
Hirota Bilinear

Utilizing the Hirota bilinear method, the lump solutions, the interaction solutions with the lump and the stripe solitons, the breathers and the rogue waves for a (3[Formula: see text]+[Formula: see text]1)-dimensional Kudryashov–Sinelshchikov equation are constructed. Two types of interaction solutions between the lumps and the stripe solitons are exhibited. Some different breathers are given by choosing special parameters in the expressions of the solitons. Through a long wave limit of breathers, the lumps and rogue waves are derived.

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