General soliton solutions for nonlinear dispersive waves in convective type instabilities

2006 ◽  
Vol 74 (3) ◽  
pp. 384-393 ◽  
Author(s):  
A H Khater ◽  
D K Callebaut ◽  
A R Seadawy
Keyword(s):  
Soliton Solutions ◽  
Dispersive Waves

Resonance Y-shaped soliton and interaction solutions in the (2 + 1)-dimensional B-type Kadomtsev–Petviashvili equation

2021 ◽  
pp. 2150222
Author(s):  
Miaomiao Wang ◽  
Zequn Qi ◽  
Junchao Chen ◽  
Biao Li
Keyword(s):  
Fluid Mechanics ◽  
Soliton Solutions ◽  
Complex Interaction ◽  
Dispersive Waves ◽  
Interaction Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Local Wave ◽  
Bkp Equation ◽  
Interaction Phenomenon

The ([Formula: see text])-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is utilized to depict weakly dispersive waves propagating in the fluid mechanics. According to [Formula: see text]-soliton solutions, resonance Y-shaped soliton and its interaction with other local wave solutions of the ([Formula: see text])-dimensional BKP equation are derived by introducing the constraint conditions. These types of hybrid soliton solutions exhibit the complex interaction phenomenon among resonance Y-shaped solitons, breather waves, line solitary waves and high-order lump waves. The dynamic behaviors of such interaction solutions are analyzed and illustrated.

Travelling Wave Solutions of Nonlinear Evolution Equation by Using an Auxiliary Elliptic Equation Method

2012 ◽  
Vol 166-169 ◽  
pp. 3228-3232 ◽  
Author(s):  
Chun Huan Xiang
Keyword(s):  
Elliptic Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Nonlinear Differential Equations ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Equation Method ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Dispersive Waves

The Camassa-Holm and Degasperis-Procesi equation describing unidirectional nonlinear dispersive waves in shallow water is reconsidered by using an auxiliary elliptic equation method. Detailed analysis of evolution solutions of the equation is presented. Some entirely new periodic-soliton solutions, include Jacobi elliptic function solutions, hyperbolic solutions and trigonal solutions, are obtained. The employed auxiliary elliptic equation method is powerful and can be also applied to solve other nonlinear differential equations. This method adds a new route to explore evolution solutions of nonlinear differential equation.

scholarly journals Construction of abundant novel analytical solutions of the space–time fractional nonlinear generalized equal width model via Riemann–Liouville derivative with application of mathematical methods

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 657-668
Author(s):  
Aly R. Seadawy ◽  
Asghar Ali ◽  
Saad Althobaiti ◽  
Khaled El-Rashidy
Keyword(s):  
Differential Equation ◽  
Soliton Solutions ◽  
Magnetic Interaction ◽  
Space Time ◽  
Auxiliary Equation ◽  
Mathematical Methods ◽  
Nonlinear Fractional Differential Equation ◽  
Dispersive Waves ◽  
Composite Function ◽  
Liouville Derivative

Abstract The space–time fractional generalized equal width (GEW) equation is an imperative model which is utilized to represent the nonlinear dispersive waves, namely, waves flowing in the shallow water strait, one-dimensional wave origination escalating in the nonlinear dispersive medium approximation, gelid plasma, hydro magnetic waves, electro magnetic interaction, etc. In this manuscript, we probe advanced and broad-spectrum wave solutions of the formerly betokened model with the Riemann–Liouville fractional derivative via the prosperously implementation of two mathematical methods: modified elongated auxiliary equation mapping and amended simple equation methods. The nonlinear fractional differential equation (NLFDE) is renovated into ordinary differential equation by the composite function derivative and the chain rule putting together along with the wave transformations. We acquire several types of exact soliton solutions by setting specific values of the personified parameters. The proposed schemes are expedient, influential, and computationally viable to scrutinize notches of NLFDEs.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

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

scholarly journals Dispersive MHD waves and alfvenons in charge non-neutral plasmas

2008 ◽  
Vol 15 (4) ◽  
pp. 681-693 ◽  
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.

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

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

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

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.

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.

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