Browsing by Author "Barman, Hemonta Kumar"

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Citation - WoS: 31
Citation - Scopus: 28
Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation
(Elsevier, 2020) Barman, Hemonta Kumar; Seadawy, Aly R.; Akbar, M. Ali; Baleanu, Dumitru; 56389; Matematik
The Riemann wave equation and the Novikov-Veselov equation are interesting nonlinear equations in the sphere of tidal and tsunami waves in ocean, river, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, homogeneous and stationary media etc. In this article, the generalized Kudryashov method is executed to demonstrate the applicability and effectiveness to extract travelling and solitary wave solutions of higher order nonlinear evolution equations (NLEEs) via the earlier stated equations. The technique is enucleated to extract solitary wave solutions in terms of trigonometric, hyperbolic and exponential function. We acquire bell shape soliton, consolidated bell shape soliton, compacton, singular kink soliton, flat kink shape soliton, smooth singular soliton and other types of soliton solutions by setting particular values of the embodied parameters. For the precision of the result, the solutions are graphically illustrated in 3D and 2D. The analytic solutions greatly facilitate the verification of numerical solvers on the stability analysis of the solution.
Citation - WoS: 31
Citation - Scopus: 36
Physically significant wave solutions to the Riemann wave equations and the Landau-Ginsburg-Higgs equation
(Elsevier, 2021) Barman, Hemonta Kumar; Aktar, Most Shewly; Uddin, M. Hafiz; Akbar, M. Ali; Baleanu, Dumitru; Osman, M. S.; 56389; Matematik
The nonlinear Riemann wave equations (RWEs) and the Landau-Ginsburg-Higgs (LGH) equation are related to plasma electrostatic waves, ion-cyclotron wave electrostatic potential, superconductivity, and drift coherent ioncyclotron waves in centrifugally inhomogeneous plasma. In this article, the interactions between the maximum order linear and nonlinear factors are balanced to compute realistic soliton solutions to the formerly stated equations in terms of hyperbolic functions. The linear and nonlinear effects rheostat the structure of the wave profiles, which vary in response to changes in the subjective parameters combined with the solutions. The established solutions to the aforementioned models using the extended tanh scheme are descriptive, typical, and consistent, and include standard soliton shapes such as bright soliton, dark soliton, compacton, peakon, periodic, and others that can be used to analyze in ion-acoustic and magneto-sound waves in plasma, homogeneous, and stationary media, particularly in the propagation of tidal and tsunami waves.