On the numerical investigation of the interaction in plasma between (high & low) frequency of (Langmuir & ion-acoustic) waves

Abstract In this paper, the Zakharov (Z.) equation in the dimensionless form is numerically investigated via (Cubic & Quantic & Septic) B-spline schemes to demonstrate the fidelity of the calculated computational solutions. The Z equation depicts the interaction in plasma between (high & low) frequency of (Langmuir & ion-acoustic) waves. This interaction is expounded in the prompts of the coastal engineering, electromagnetic field, signal handling in the optical fibres, plasma physics, and fluid dynamics. Three different computational schemes were applied to the Z equation for constructing many novel analytical solutions. In our paper, we try to check the accuracy of these solutions via the above-mentioned numerical schemes. Moreover, some separate sketches are given to indicate more physical features of this interaction. The originality of the obtained solutions is investigated by showing the similarities and differences between our obtained solutions and that was purchased in previously published papers.

[1]  Peng Zhang,et al.  A review of the composite phase change materials: Fabrication, characterization, mathematical modeling and application to performance enhancement , 2016 .

[2]  M. Khater,et al.  On exact and approximate solutions of (2+1)-dimensional Konopelchenko-Dubrovsky equation via modified simplest equation and cubic B-spline schemes , 2019, Thermal Science.

[3]  N. Ali,et al.  Optical soliton solutions to the (2+1)$(2+1)$-dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation , 2019, Advances in Difference Equations.

[4]  J. P. Jaiswal,et al.  Stability analysis of fourth-order iterative method for finding multiple roots of non-linear equations , 2019, Applied Mathematics and Nonlinear Sciences.

[5]  Gui-Quan Sun,et al.  Mathematical modeling of population dynamics with Allee effect , 2016, Nonlinear Dynamics.

[6]  J. R. Bogning,et al.  Modeling Nonlinear Partial Differential Equations and Construction of Solitary Wave Solutions in an Inductive Electrical Line , 2019, Journal of Advances in Mathematics and Computer Science.

[7]  Mostafa M. A. Khater,et al.  Abundant new solutions of the transmission of nerve impulses of an excitable system , 2020, The European Physical Journal Plus.

[8]  Andreas Loukas,et al.  A Time-Vertex Signal Processing Framework: Scalable Processing and Meaningful Representations for Time-Series on Graphs , 2017, IEEE Transactions on Signal Processing.

[9]  M. Khater,et al.  Optical wave solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term via modified Khater method , 2020 .

[10]  Changbum Chun,et al.  A constructive method for solving the equation Xa=b in Rn: A generalization of division in Rn , 2020, Appl. Math. Comput..

[11]  Feng Gao,et al.  A new technology for solving diffusion and heat equations , 2017 .

[12]  H. M. Baskonus,et al.  Optical Soliton Solutions of the Cubic-Quartic Nonlinear Schrödinger and Resonant Nonlinear Schrödinger Equation with the Parabolic Law , 2019, Applied Sciences.

[13]  Sebastian Schöps,et al.  Solving Nonlinear Circuits With Pulsed Excitation by Multirate Partial Differential Equations , 2017, IEEE Transactions on Magnetics.

[14]  Mostafa M. A. Khater,et al.  Computational and numerical simulations for the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation , 2020, Physica Scripta.

[15]  Maziar Raissi,et al.  Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations , 2018, J. Mach. Learn. Res..

[16]  Behzad Ghanbari,et al.  A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing , 2020 .

[17]  T. Allahviranloo,et al.  On the fuzzy fractional differential equation with interval Atangana–Baleanu fractional derivative approach , 2020 .

[18]  Liguo Chen,et al.  Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas , 2020, Complex..

[19]  Yarema Yaroslavovich Rushchitskii,et al.  Cubically Nonlinear Elastic Waves: Wave Equations and Methods of Analysis , 2003 .

[20]  C. Cattani,et al.  Periodic, complex and kink-type solitons for the nonlinear model in microtubules , 2019 .

[21]  Anjan Biswas,et al.  1-soliton solution of the Zakharov–Kuznetsov equation with dual-power law nonlinearity , 2009 .

[22]  M. Khater,et al.  Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method , 2017 .

[23]  C. Cattani,et al.  Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation , 2020 .

[24]  Peter A. E. M. Janssen,et al.  The Intermediate Water Depth Limit of the Zakharov Equation and Consequences for Wave Prediction , 2007 .

[25]  Xian-lin Yang,et al.  Explicit exact solutions for the generalized Zakharov equations with nonlinear terms of any order , 2009, Comput. Math. Appl..

[26]  E. V. Krishnan,et al.  Solitons and cnoidal waves of the Klein–Gordon–Zakharov equation in plasmas , 2012 .

[27]  M. A. Abdou.  An analytical method for space–time fractional nonlinear differential equations arising in plasma physics , 2017 .

[28]  Behzad Ghanbari,et al.  A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative , 2020 .

[29]  Dianchen Lu,et al.  Analytical and numerical solutions for the current and voltage model on an electrical transmission line with time and distance , 2020, Physica Scripta.

[30]  H. Rezazadeh,et al.  Periodic waves of the non dissipative double dispersive micro strain wave in the micro structured solids , 2020 .

[32]  Dianchen Lu,et al.  The plethora of explicit solutions of the fractional KS equation through liquid–gas bubbles mix under the thermodynamic conditions via Atangana–Baleanu derivative operator , 2020, Advances in Difference Equations.

[33]  Xiaojun Yin,et al.  Dynamics of nonlinear Rossby waves in zonally varying flow with spatial-temporal varying topography , 2019, Appl. Math. Comput..

[34]  Shuai Yao,et al.  The stationary quantum Zakharov system perturbed by a local nonlinearity , 2019, Appl. Math. Lett..

[35]  Yu Yang,et al.  A multiquadric quasi-interpolations method for CEV option pricing model , 2019, J. Comput. Appl. Math..

[36]  Adem C. Cevikel,et al.  New exact solutions of the space-time fractional KDV burgers and nonlinear fractional foam drainage equation , 2017 .

[37]  Dan Liu,et al.  An effective feature extraction method by power spectral density of EEG signal for 2-class motor imagery-based BCI , 2018, Medical & Biological Engineering & Computing.

[38]  Hai Lin.  Electronic structure from equivalent differential equations of Hartree–Fock equations , 2019, Chinese Physics B.

[39]  Ruigang Zhang,et al.  A new model equation for nonlinear Rossby waves and some of its solutions , 2019, Physics Letters A.

[40]  H. M. Baskonus,et al.  New Complex and Hyperbolic Forms for Ablowitz–Kaup–Newell–Segur Wave Equation with Fourth Order , 2019, Applied Mathematics and Nonlinear Sciences.

[41]  K. Parand,et al.  A hybrid numerical method to solve nonlinear parabolic partial differential equations of time-arbitrary order , 2019, Comput. Appl. Math..

[42]  Shahzad Sarwar,et al.  Novel explicit solutions for the nonlinear Zoomeron equation by using newly extended direct algebraic technique , 2020 .

[43]  Yunjiao Li,et al.  Enhancement on structural stability of Ni-rich cathode materials by in-situ fabricating dual-modified layer for lithium-ion batteries , 2019, Nano Energy.

[44]  Ahmad T. Ali,et al.  Abundant numerical and analytical solutions of the generalized formula of Hirota-Satsuma coupled KdV system , 2020 .

[45]  Abdul-Majid Wazwaz,et al.  The extended tanh method for abundant solitary wave solutions of nonlinear wave equations , 2007, Appl. Math. Comput..

[46]  Mostafa M. A. Khater,et al.  The new structure of analytical and semi-analytical solutions of the longitudinal plasma wave equation in a magneto-electro-elastic circular rod , 2020, Modern Physics Letters B.

[47]  Mostafa M. A. Khater,et al.  Analytical, semi-analytical, and numerical solutions for the Cahn–Allen equation , 2020 .

[48]  M. A. Abdou,et al.  Analytical and semi-analytical ample solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term , 2020 .

[49]  R. Agarwal,et al.  A study of fractional Lotka‐Volterra population model using Haar wavelet and Adams‐Bashforth‐Moulton methods , 2020, Mathematical Methods in the Applied Sciences.

[50]  Rosario Miceli,et al.  Experimental Study on B-Spline-Based Modulation Schemes Applied in Multilevel Inverters for Electric Drive Applications , 2019, Energies.

[51]  R. Ansari,et al.  Modified Kudryashov method for solving the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities , 2017 .

[52]  T. Sagiya,et al.  Shear strain concentration mechanism in the lower crust below an intraplate strike-slip fault based on rheological laws of rocks , 2016, Earth, Planets and Space.

[53]  M. Khater,et al.  Approximate Simulations for the Non-linear Long-Short Wave Interaction System , 2020, Frontiers of Physics.

[54]  Haci Mehmet Baskonus,et al.  New complex wave patterns to the electrical transmission line model arising in network system , 2020 .

[55]  T. Hayat,et al.  A study on the convergence conditions of generalized differential transform method , 2017 .