Authors:
M. Al-Amin ,M. Nurul Islam,DOI NO:
https://doi.org/10.26782/jmcms.2023.07.00003Keywords:
The nonlinear Landau-Ginsberg-Higgs (LGH) model,the generalized exponential rational function method (GERFM),the traveling wave transformation,the soliton solutions,Abstract
In this study, the nonlinear Landau-Ginsberg-Higgs (LGH) model is proposed and examined. The stated model is applied to analyze superconductivity and drift cyclotron waves in radially inhomogeneous plasma for coherent ion-cyclotron waves. This is undeniably a robust mathematical model in real-world applications. The generalized exponential rational function method (GERFM) is utilized to extract the suitable, useful, and further general solitary wave solutions of the LGH model via the traveling wave transformation. Furthermore, we investigate the effects of wave velocity in a particular time limit through a graphical representation of the examined solutions of the model to understand the dynamic behavior of the system. The attained results confirm the effectiveness and reliability of the considered schemeRefference:
I. A.S.H.F. Mohammed, H.O. Bakodah, M.A. Banaja, A.A. Alshaery, Q. Zhou, A. Biswas, P. Seithuti. Moshokoa, M.R. Belic, Bright optical solitons of Chen-Lee-Liu equation with improved Adomian decomposition method, Optik, 181:964-970, 2019.
II. A. Zafar, H. Rezazadeh, K.K. Ali, On finite series solutions of conformable time-fractional Cahn-Allen equation, Nonlin. Eng., 9(1):194-200, 2020.
III. A. Yusuf, M. Inc, A.I. Aliyu, D. Baleanu, Optical Solitons Possessing Beta Derivative of the Chen-Lee-Liu Equation in Optical Fibers, Fron. Phys., 7, 34, 2019.
IV. A.S.H.F. Mohammed, H.O. Bakodah, Approximate Solutions for Dark and Singular Optical Solitons of Chen-Lee-Liu Model by Adomian-based Methods, Int. J. Appl. Comput. Math., 7, 98, 2021.
V. A. Bekir, O. Unsal, Exact solutions for a class of nonlinear wave equations by using first integral method, Int. J. Nonlin. Sci., 15(2):99-110, 2013.
VI. A. Irshad, S.T. Mohyud-Din, N. Ahmed, U. Khan, A new modification in simple equation method and its applications on nonlinear equations of physical nature, Results Phys., 7:4232-40, 2017.
VII. A.C. Cevikel, E. Aksoy, O. Guner, A. Bekir, Dark bright soliton solutions for some evolution equations, Int. J. Nonlin. Sci., 16(3):195-202, 2013.
VIII. A. Iftikhar, A. Ghafoor, T. Zubair, S. Firdous, S.T. Mohyud-Din, (????′????⁄,1????⁄)-Expansion method for traveling wave solutions of (2+1) dimensional generalized KdV, Sine Gordon and Landau-Ginzburg-Higgs equations, Sci. Res. Essays., 8(28):1349-59, 2013.
IX. B. Ghanbari, D. Baleanu, M.A. Qurashi, New Exact Solutions of the Generalized Benjamin-Bona-Mahony Equation, Symmetry, 11(1):20, 2019.
X. B. Ghanbari, M.S. Osman, D. Baleanu, Generalized exponential rational function method for extended Zakharov Kuzetsov equation with conformable derivative, Mod. Phy. Lett. A., 34,1950155,16pp, 2019.
XI. B. Ghanbari, M. Inc, A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear schrödinger equation, Eur. Phys. J. Plus, 133(4):142, 18pp, 2018.
XII. E.H.M. Zahran, M.M.A. Khater, Modified extended tanh-function method and its applications to the Bogoyavlenskii equation, Appl. Math. Model, 40(3):1769-1775, 2017.
XIII. F.S. Khodadad, S.M.M. Alizamini, B. Günay, L. Akinyemi, H. Rezazadeh, I. Mustafa, Abundant optical solitons to the Sasa-Satsuma higher-order nonlinear Schrödinger equation, Opt. Quant. Elec., 53, 702, 2021. XIV. H. Rezazadeh, A. Korkmaz, M. Eslami, S.M.M. Alizamini, A large family of optical solutions to Kundu-Eckhaus model by a new auxiliary equation method, Opt. Quant. Elec., 51(84), 2019.
XV. H.M. Baskonus, H. Bulut, T.A. Sulaiman, New complex hyperbolic structures to the Lonngren-Wave equation by using Sine-Gordon expansion method, App. Math. Non-lin. Sci., 4(1):129-138, 2019.
XVI. H.M. Baskonus, H. Bulut, A. Atangana, On the complex and hyperbolic structures of the longitudinal wave equation in a magneto-electro-elastic circular rod, Smart Mater. Struct., 25(3):035022, 2016.
XVII. K. Ahmad, K. Bibi, M.S. Arif, K. Abodayeh, New Exact Solutions of Landau-Ginzburg-Higgs Equation Using Power Index Method, J. Func. Spa., 4351698, 6pp, 2023.
XVIII. M.M. El-Borai, W.G. El-Sayed, R.M. Al-Masroub, Exact solutions for time fractional coupled Whitham-Broer-Kaup equations via exp-function method, Int. Res. J. Eng. Tech., 2(6):307-315, 2015.
XIX. M. Al-Amin, M.N. Islam, O.A. Ilhan, M.A. Akbar, D. Soybas, Solitary Wave Solutions to the Modified Zakharov-Kuznetsov and the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schiff Models in Mathematical Physics, J. Math., 2022, 5224289, 16pp, 2022.
XX. M. Al-Amin, M.N. Islam, M.A. Akbar, Adequate wide-ranging closed-form wave solutions to a nonlinear biological model, Par. Diff. Equ. App. Math., 2021(4):100042, 2021.
XXI. M. Al-Amin, M.N. Islam, M.A. Akbar, The closed-form soliton solutions of the time-fraction Phi-four and (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff model using the recent approach, Par. Diff. Equ. App. Math., 2022(5):100374, 2022.
XXII. M.N. Islam, M.A. Akbar, Closed form solutions to the coupled space-time fractional evolution equations in mathematical physics through analytical method, J. Mech. Cont. Math. Sci., 13(2):1-23, 2018.
XXIII. M.A. Akbar, N.H.M. Ali, E.M.E. Zayed, Abundant exact traveling wave solutions of generalized Bretherton equation via improved (????′????⁄)-expansion method, Com. Theo. Phys., 57(2012):173-178, 2012.
XXIV. M.A.E. Abdel Rahman, H.A. Alkhidhr, Closed-form solutions to the conformable space-time fractional simplified MCH equation and time fractional Phi-4 equation, Results Phys., 18, 103294, 2020.
XXV. M. Bilal, W. Hu, J. Ren, Different wave structures to the Chen-Lee-Liu equation of monomode fibers and its modulation instability analysis, Eur. Phys. J. Plus, 136(4):385, 2021.
XXVI. M.E. Islam, M.A. Akbar, Stable wave solutions to the Landau-Ginzburg-Higgs equation and the modified equal width wave equation using the IBSEF method, Arab J. Basic Appl. Sci., 27(1):270-278, 2020.
XXVII. M.R. Ali, M.A. Khattab, S.M. Mabrouk, Travelling wave solution for the Landau-Ginburg-Higgs model via the inverse scattering transformation method, Nonlin. Dyn., 111:7687-7697, 2023.
XXVIII. M.N. Islam, O.A. İlhan, M.A. Akbar, F.B. Benli, D. Soybaş, Wave propagation behavior in nonlinear media and resonant nonlinear interactions, Com. Nonlin. Sci. Num. Simul., 108, 106242, 2022.
XXIX. N. Ozdemir, H. Esen, A. Secer, M. Bayram, A. Yusuf, T.A. Sulaiman, Optical Soliton Solutions to Chen Lee Liu model by the modified extended tanh expansion scheme, Optik, 245, 167643, 2021.
XXX. O.A. Ilhan, M.N. Islam, M.A. Akbar, Construction of functional closed form wave solutions to the ZKBBM equation and the Schrodinger equation, Iranian J. Sci. Tech. Transac. Mech. Eng., 2020, 14pp, 2020.
XXXI. O.G. Gaxiola, A. Biswas, W-shaped optical solitons of Chen-Lee-Liu equation by Laplace-Adomian decomposition method, Opt. Quan. Electr., 50, 314:1-11, 2018.
XXXII. R. Roy, M.A. Akbar, A.R. Seadawy, D. Baleanu, Search for adequate closed form wave solutions to space-time fractional nonlinear equations, Par. Diff. Equ. App. Math., 2021(4):100025, 2021.
XXXIII. S.J. Chen, X. Lü, X.F. Tang, Novel evolutionary behaviors of the mixed solutions to a generalized Burgers equation with variable coefficients, Commun. Nonlin. Sci. Num. Simul., 95, 105628, 2021.
XXXIV. S. Albosaily, W.W. Mohammed, A.E. Hamza, M. El-Morshedy, H. Ahmad, The exact solutions of the stochastic fractional space Allen-Cahn equation, Open Phy., 20(1):23-29, 2022. XXXV. W.X. Ma, L. Zhang, Lump solutions with higher-order rational dispersion relations, Pram. J. Phys., 94(43), 2020.
XXXVI. W.X. Ma, Y. Zhang, Y. Tang, Symbolic computation of lump solutions to a combined equation involving three types of nonlinear terms, East Asian J. Appl. Math., 10(4):732-745, 2020.
XXXVII. W. Gao, H. Rezazadeh, Z. Pinar, H.M. Baskonus, S. Sarwar, G. Yel, Novel explicit solutions for the nonlinear Zoomeron equation by using newly extended direct algebraic technique, Opt. Qua. Elec., 52(1), 2020.
XXXVIII. W.P. Hu, Z.C. Deng, S.M. Han, W. Fa, Multi symplectic Runge-Kutta method for Landau-Ginzburg-Higgs equation, Appl. Math. Mech., 30(8):1027-34, 2009.
XXXIX. Y. Yildirim, Optical solitons to Chen-Lee-Liu model in birefringent fibers with trial equation approach, Optik, 183:881-886, 2019.
XL. Y. Liu, J. Roberts, Y. Yan, A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes, Int. J. Com., 95(6-7):1151-1169, 2017.
View Download