Collision phenomena among lump, periodic and stripe soliton solutions to a (2 + 1)-dimensional Benjamin–Bona–Mahony–Burgers Model

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

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Properties of turbulence driven by random external force in the Burgers model

Uspekhi Fizicheskih Nauk ◽

10.3367/ufnr.2016.07.037865 ◽

2016 ◽

Vol 186 (12) ◽

pp. 1349-1353

Author(s):

Kirill P. Zybin ◽

Anton S. Il'yn

Keyword(s):

External Force ◽

Burgers Model

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N-fold Darboux transformation and soliton solutions for the relativistic Toda lattice equation

Authorea ◽

10.22541/au.158379383.32853181 ◽

2020 ◽

Author(s):

Fangcheng Fan ◽

Zhiguo Xu ◽

Shaoyun Shi

Keyword(s):

Darboux Transformation ◽

Toda Lattice ◽

Soliton Solutions ◽

Lattice Equation ◽

Relativistic Toda Lattice ◽

Toda Lattice Equation

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Dispersive MHD waves and alfvenons in charge non-neutral plasmas

Nonlinear Processes in Geophysics ◽

10.5194/npg-15-681-2008 ◽

2008 ◽

Vol 15 (4) ◽

pp. 681-693 ◽

Cited By ~ 3

Author(s):

K. Stasiewicz ◽

J. Ekeberg

Keyword(s):

Soliton Solutions ◽

Theoretical Models ◽

Mhd Waves ◽

Space Plasmas ◽

Charge Effects ◽

Novel Technique ◽

Solitary Structures ◽

Spatial Dimensions ◽

Electric Potentials ◽

Linear And Nonlinear

Abstract. Dispersive properties of linear and nonlinear MHD waves, including shear, kinetic, electron inertial Alfvén, and slow and fast magnetosonic waves are analyzed using both analytical expansions and a novel technique of dispersion diagrams. The analysis is extended to explicitly include space charge effects in non-neutral plasmas. Nonlinear soliton solutions, here called alfvenons, are found to represent either convergent or divergent electric field structures with electric potentials and spatial dimensions similar to those observed by satellites in auroral regions. Similar solitary structures are postulated to be created in the solar corona, where fast alfvenons can provide acceleration of electrons to hundreds of keV during flares. Slow alfvenons driven by chromospheric convection produce positive potentials that can account for the acceleration of solar wind ions to 300–800 km/s. New results are discussed in the context of observations and other theoretical models for nonlinear Alfvén waves in space plasmas.

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Onset of the broad-ranging general stable soliton solutions of nonlinear equations in physics and gas dynamics

Results in Physics ◽

10.1016/j.rinp.2020.103762 ◽

2021 ◽

Vol 20 ◽

pp. 103762

Author(s):

Md. Abdul Kayum ◽

Shamim Ara ◽

M.S. Osman ◽

M. Ali Akbar ◽

Khaled A. Gepreel

Keyword(s):

Nonlinear Equations ◽

Gas Dynamics ◽

Soliton Solutions

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Lie symmetry analysis for complex soliton solutions of coupled complex short pulse equation

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7105 ◽

2021 ◽

Author(s):

Vikas Kumar ◽

Abdul‐Majid Wazwaz

Keyword(s):

Short Pulse ◽

Soliton Solutions ◽

Lie Symmetry ◽

Symmetry Analysis ◽

Lie Symmetry Analysis ◽

Short Pulse Equation

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N-soliton solutions and the Hirota conditions in (1 + 1)-dimensions

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2020-0214 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Wen-Xiu Ma

Keyword(s):

Common Factors ◽

Soliton Solutions ◽

Higher Order ◽

Kdv Equations ◽

The Common ◽

Bilinear Formulation ◽

Generalized Kdv Equations ◽

Hirota Bilinear

Abstract We analyze N-soliton solutions and explore the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations, within the Hirota bilinear formulation. An algorithm to verify the Hirota conditions is proposed by factoring out common factors out of the Hirota function in N wave vectors and comparing degrees of the involved polynomials containing the common factors. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, together with all proofs of the existence of N-soliton solutions to all equations in two classes.

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

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0186 ◽

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.

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