The new structure of analytical and semi-analytical solutions of the longitudinal plasma wave equation in a magneto-electro-elastic circular rod

This research paper extracts novel analytical and semi-analytical wave solutions of the longitudinal wave equation in a magneto-electro-elastic circular rod by using the modified Khater method as one of the most novel and general computational methods and the Adomian decomposition method as a semi-analytical method. The longitudinal waves in metallic thin films are explained for the first time by Nilsson and Lindau, who used the visual evidence. They noted subdued anomalies in the ports of thin ([Formula: see text]100 Å) Ag layers deposited on amorphous silica for p-polarized light at frequencies padlock to the dynamic plasma frequency. These properties are studied by our two suggested methods and are explained by sketching some of our obtained solutions. Moreover, the stability property is tested for our obtained solutions by using the features of the Hamiltonian system. The performance of our used methods shows the power and effectiveness of these methods and their ability to apply on many different forms of nonlinear partial differential equations.

[1]  Roderick Boswell.  Very efficient plasma generation by whistler waves near the lower hybrid frequency , 1984 .

[2]  M. Kaplan,et al.  Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method , 2015 .

[3]  Optical solitons for the Kundu–Eckhaus equation with time dependent coefficient , 2018 .

[4]  Mostafa M. A. Khater,et al.  Bifurcations of traveling wave solutions for Dodd–Bullough–Mikhailov equation and coupled Higgs equation and their applications , 2017 .

[5]  Mostafa M. A. Khater,et al.  Explicit Lump Solitary Wave of Certain Interesting (3+1)-Dimensional Waves in Physics via Some Recent Traveling Wave Methods , 2019, Entropy.

[6]  Alain Bensoussan,et al.  Stochastic Navier-Stokes Equations , 1995 .

[7]  G. Zaman,et al.  THE ADOMIAN DECOMPOSITION METHOD FOR SOLVING HIV INFECTION MODEL OF LATENTLY INFECTED CELLS , 2019, Matrix Science Mathematic.

[8]  Ebru Cavlak Aslan,et al.  Optical soliton solutions of the NLSE with quadratic-cubic-Hamiltonian perturbations and modulation instability analysis , 2019, Optik.

[9]  S J Tendler,et al.  Surface plasmon resonance analysis of dynamic biological interactions with biomaterials. , 2000, Biomaterials.

[10]  Mostafa M. A. Khater,et al.  Modified extended tanh-function method and its applications to the Bogoyavlenskii equation , 2016 .

[11]  Adem C. Cevikel,et al.  New exact travelling wave solutions of nonlinear physical models , 2009 .

[12]  Ahmet Bekir,et al.  Application of the Exp-function method for nonlinear differential-difference equations , 2010, Appl. Math. Comput..

[13]  Mostafa M. A. Khater,et al.  Solitary Wave Solutions of the Benjamin-BonaMahoney-Burgers Equation with Dual Power-Law Nonlinearity , 2017 .

[14]  W. Wyss.  The fractional diffusion equation , 1986 .

[15]  Adem C. Cevikel,et al.  Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method , 2015 .

[16]  Dipankar Kumar,et al.  New exact solutions for the time fractional coupled Boussinesq–Burger equation and approximate long water wave equation in shallow water , 2017 .

[17]  D. Baleanu,et al.  Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations , 2018, Chaos, Solitons & Fractals.

[18]  D. Baleanu,et al.  Optical solitons and stability analysis with spatio-temporal dispersion in Kerr and quadric-cubic nonlinear media , 2019, Optik.

[19]  Mostafa M. A. Khater,et al.  Solitary wave solutions for the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation , 2016 .

[20]  Lawrence Kuhn,et al.  ERRATA: GRATING COUPLER FOR EFFICIENT EXCITATION OF OPTICAL GUIDED WAVES IN THIN FILMS , 1970 .

[21]  L. O. Svaasand,et al.  Boundary conditions for the diffusion equation in radiative transfer. , 1994, Journal of the Optical Society of America. A, Optics, image science, and vision.

[22]  R. Temam.  Navier-Stokes Equations , 1977 .

[23]  Mostafa M. A. Khater,et al.  Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation , 2017 .

[24]  Zeliha Korpinar,et al.  Numerical simulations for fractional variation of (1 + 1)-dimensional Biswas-Milovic equation , 2018, Optik.

[25]  G. Swaters,et al.  Introduction to Hamiltonian Fluid Dynamics and Stability Theory , 1999 .

[26]  M. Belić,et al.  Gray and black optical solitons with quintic nonlinearity , 2018 .

[27]  Francis F. Chen,et al.  Plasma ionization by helicon waves , 1991 .

[28]  P. Moin,et al.  Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , 1984 .

[29]  Ahmet Bekir,et al.  On traveling wave solutions to combined KdV–mKdV equation and modified Burgers–KdV equation , 2009 .

[30]  F. Mainardi.  The fundamental solutions for the fractional diffusion-wave equation , 1996 .

[31]  Marek Capiński,et al.  Stochastic Navier-Stokes equations , 1991 .

[32]  Mostafa M. A. Khater,et al.  Dispersive long wave of nonlinear fractional Wu-Zhang system via a modified auxiliary equation method , 2019, AIP Advances.

[33]  M. Khater,et al.  Bifurcations of new multi soliton solutions of the van der Waals normal form for fluidized granular matter via six different methods , 2017 .

[34]  M. Kaplan,et al.  Auxiliary Equation Method for Fractional Differential Equations with Modified Riemann–Liouville Derivative , 2016 .

[35]  Ahmet Bekir,et al.  Analytic solutions of the (2 + 1)-dimensional nonlinear evolution equations using the sine-cosine method , 2009, Appl. Math. Comput..

[36]  Aly R. Seadawy,et al.  New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod , 2018 .

[37]  Ahmet Bekir,et al.  Bright and dark soliton solutions for some nonlinear fractional differential equations , 2016 .

[38]  K. Usadel,et al.  GENERALIZED DIFFUSION EQUATION FOR SUPERCONDUCTING ALLOYS. , 1970 .

[39]  Dipankar Kumar,et al.  New optical solitons of cubic-quartic nonlinear Schrödinger equation , 2018 .

[40]  Mostafa M. A. Khater,et al.  New wave solutions for the fractional-order biological population model, time fractional burgers, Drinfel’d–Sokolov–Wilson and system of shallow water wave equations and their applications , 2017 .

[41]  Dianchen Lu,et al.  Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation , 2019, Mathematical and Computational Applications.

[42]  T. Harko,et al.  Computation of the General Relativistic Perihelion Precession and of Light Deflection via the Laplace-Adomian Decomposition Method , 2018, Advances in High Energy Physics.

[43]  J. Alami,et al.  Plasma dynamics in a highly ionized pulsed magnetron discharge , 2005 .

[44]  M. Khater,et al.  Bifurcations of solitary wave solutions for the three dimensional Zakharov–Kuznetsov–Burgers equation and Boussinesq equation with dual dispersion , 2017 .

[45]  Dumitru Baleanu,et al.  A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives , 2018, Chaos, Solitons & Fractals.

[46]  Mostafa M. A. Khater,et al.  Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions , 2018, Mathematical and Computational Applications.

[47]  A. U. Keskin.  Adomian Decomposition Method (ADM) , 2019, Boundary Value Problems for Engineers.

[48]  A. Atangana,et al.  On the complex and hyperbolic structures of the longitudinal wave equation in a magneto-electro-elastic circular rod , 2016 .

[49]  Monique Y. Leclerc,et al.  Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation , 1990 .

[50]  Ahmed A. Hamoud,et al.  Modified Adomian Decomposition Method for Solving Fuzzy Volterra-Fredholm Integral Equation , 2018 .