New Application for Generalized Regularized Long Wave (GRLW) Equation, Modified Dispersive Water Wave (MDWW) Equation and Kawahara Equation by Homogeneous Balance Method

Taha, Wafaa M.; Ibrahim, Israa A.; Noorani, Mohd Salmi Md

doi:10.36478/jeasci.2019.4010.4017

Cited by 2 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The homogeneous balance method is described in [21][22][23]. For a partial differential equation is a solution of equation (1).…”

Section: Homogeneous Balance Methodsmentioning

confidence: 99%

Novel solutions of (2+1) dimensional modified Bogoyavlenskii’s breaking soliton equation with variable coefficients

Wang

2023

Phys. Scr.

View full text Add to dashboard Cite

In this paper, a (2+1)-dimensional breaking soliton equation is described. Firstly, the exact solution of the equation is constructed by the homogeneous equilibrium method. and the double soliton solutions with arbitrary functions are obtained. Second, the basic law of interaction between the different solitons are revealed and some new local structures are addressed by using the auxiliary equation method and the elliptic equation and the corresponding transformation, the infinite sequence exact solution of the generalized form equation of the breaking soliton equation is derived. Sinusoidal solitons, parabolic solitons and folded solitons of arbitrary shape propagating with variable speed are considered. In addition, by analyzing the infinite sequence of exact solutions given by the transformation of elliptic equation, the inner law between the exact solutions of the breaking soliton equation are also discussed.

show abstract

“…The homogeneous balance method is described in [21][22][23]. For a partial differential equation is a solution of equation (1).…”

Section: Homogeneous Balance Methodsmentioning

confidence: 99%

Novel solutions of (2+1) dimensional modified Bogoyavlenskii’s breaking soliton equation with variable coefficients

Wang

2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

Simulation Studies on the Dissipative Modified Kawahara Solitons in a Complex Plasma

et al. 2022

View full text Add to dashboard Cite

In this work, a damped modified Kawahara equation (mKE) with cubic nonlinearity and two dispersion terms including the third- and fifth-order derivatives is analyzed. We employ an effective semi-analytical method to achieve the goal set for this study. For this purpose, the ansatz method is implemented to find some approximate solutions to the damped mKE. Based on the proposed method, two different formulas for the analytical symmetric approximations are formally obtained. The derived formulas could be utilized for studying all traveling waves described by the damped mKE, such as symmetric solitary waves (SWs), shock waves, cnoidal waves, etc. Moreover, the energy of the damped dressed solitons is derived. Furthermore, the obtained approximations are used for studying the dynamics of the dissipative dressed (modified Kawahara (mK)) dust-ion acoustic (DIA) solitons in an unmagnetized collisional superthermal plasma consisting of inertia-less superthermal electrons and inertial cold ions as well as immobile negative dust grains. Numerically, the impact of the collisional parameter that arises as a result of taking the ion-neutral collisions into account and the electron spectral index on the profile of the dissipative structures are examined. Finally, the analytical and numerical approximations using the finite difference method (FDM) are compared in order to confirm the high accuracy of the obtained approximations. The achieved results contribute to explaining the mystery of several nonlinear phenomena that arise in different plasma physics, nonlinear optics, shallow water waves, oceans, and seas, and so on.

show abstract

New Application for Generalized Regularized Long Wave (GRLW) Equation, Modified Dispersive Water Wave (MDWW) Equation and Kawahara Equation by Homogeneous Balance Method

Cited by 2 publications

References 0 publications

Novel solutions of (2+1) dimensional modified Bogoyavlenskii’s breaking soliton equation with variable coefficients

Novel solutions of (2+1) dimensional modified Bogoyavlenskii’s breaking soliton equation with variable coefficients

Simulation Studies on the Dissipative Modified Kawahara Solitons in a Complex Plasma

Contact Info

Product

Resources

About