Harmonizing wave solutions to the Fokas-Lenells model through the generalized Kudryashov method

Abstract In this article, the closed form general and standard solutions accessible in the literature of nonlinear evolution equation (NLEE), namely, the Fokas-Lenells (FL) equation is established by using the generalized Kudryashov approach. The implemented method extracts lots of new and compatible wave solutions involving unknown parameters and expressed in terms of exponential, trigonometric and hyperbolic functions. We explain the physical meaning of geometrical structures for some derived solutions by assigning definite values of the unspecified parameters. As an aftermath, diverse wave shapes including kink wave shape, flat kink wave shape, bell shape, anti-bell shape, singular bell shape along with bright, dark, singular solitary wave envelopes are properly developed. These nonlinear wave envelopes are frequently applicable in optical fibers. It has been established that the assigned techniques are general, efficient and straightforward and also it can be exerted to accomplish closed form solutions of diverse NLEEs originated in mathematical physics and engineering fields.

[1]  N. Kudryashov.  Highly dispersive optical solitons of the generalized nonlinear eighth-order Schrödinger equation , 2020 .

[2]  N. Kudryashov.  Construction of nonlinear differential equations for description of propagation pulses in optical fiber , 2019, Optik.

[3]  Fethi Bin Muhammad Belgacem,et al.  Applications of the novel (G′/G) expansion method to find new exact traveling wave solutions of the nonlinear coupled Higgs field equation , 2015 .

[4]  Nikolai A. Kudryashov,et al.  Exact solutions of the equation for surface waves in a convecting fluid , 2019, Appl. Math. Comput..

[5]  Rubayyi T. Alqahtani,et al.  Optical soliton perturbation with full nonlinearity for Fokas–Lenells equation , 2018, Optik.

[6]  D. Baleanu,et al.  Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation , 2020 .

[7]  N. Kudryashov.  Optical solitons of mathematical model with arbitrary refractive index , 2020 .

[8]  K. Hosseini,et al.  New exact solutions of the coupled sine-Gordon equations in nonlinear optics using the modified Kudryashov method , 2018 .

[9]  W. Hereman,et al.  The tanh method: II. Perturbation technique for conservative systems , 1996 .

[10]  A. Biswas,et al.  Optical soliton perturbation with Fokas–Lenells equation by mapping methods , 2019, Optik.

[11]  A. Biswas,et al.  Optical soliton perturbation with Fokas-Lenells model by Riccati equation approach , 2018, Optik.

[12]  A. Wazwaz,et al.  Exact wave solutions for the nonlinear time fractional Sharma–Tasso–Olver equation and the fractional Klein–Gordon equation in mathematical physics , 2017 .

[13]  Abdul-Majid Wazwaz,et al.  The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations , 2005, Appl. Math. Comput..

[14]  M. Osman,et al.  New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method , 2020, Alexandria Engineering Journal.

[15]  M. Belić,et al.  Optical soliton perturbation of Fokas–Lenells equation with two integration schemes , 2018, Optik.

[16]  Jian‐Guo Liu,et al.  A variety of nonautonomous complex wave solutions for the (2+1)-dimensional nonlinear Schrödinger equation with variable coefficients in nonlinear optical fibers , 2019, Optik.

[17]  M. Akbar,et al.  Soliton solutions to voltage analysis in nonlinear electrical transmission lines and electric signals in telegraph lines , 2020 .

[18]  N. Kudryashov.  Highly dispersive optical solitons of equation with various polynomial nonlinearity law , 2020 .

[19]  M. Belić,et al.  Optical soliton perturbation with Fokas–Lenells equation using three exotic and efficient integration schemes , 2018, Optik.

[20]  J. Manafian,et al.  Application of the generalized G′/G-expansion method for nonlinear PDEs to obtaining soliton wave solution , 2017 .

[21]  En-Gui Fan,et al.  Traveling wave solutions for nonlinear equations using symbolic computation , 2002 .

[22]  S. Y. Doka,et al.  Chirped soliton solutions of Fokas–Lenells equation with perturbation terms and the effect of spatio-temporal dispersion in the modulational instability analysis , 2020 .

[23]  A. Biswas,et al.  Dispersive Optical Solitons in Nanofibers with Schrödinger-Hirota Equation , 2016 .

[24]  Anjan Biswas,et al.  Optical soliton perturbation, group invariants and conservation laws of perturbed Fokas–Lenells equation , 2018, Chaos, Solitons & Fractals.

[25]  W. Hereman,et al.  The tanh method: I. Exact solutions of nonlinear evolution and wave equations , 1996 .

[26]  M. M. Rahman.  The Generalized Kudryashov Method: a Renewed Mechanism for Performing Exact Solitary Wave Solutions of Some NLEEs , 2019, JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES.

[27]  M. Belić,et al.  Optical solitons with polarization-mode dispersion for coupled Fokas–Lenells equation with two forms of integration architecture , 2018, Optical and Quantum Electronics.

[28]  Abdul-Majid Wazwaz,et al.  A sine-cosine method for handlingnonlinear wave equations , 2004, Math. Comput. Model..

[29]  M. Osman,et al.  Competent closed form soliton solutions to the nonlinear transmission and the low-pass electrical transmission lines , 2020, The European Physical Journal Plus.

[30]  A. Biswas.  Chirp-free bright optical soliton perturbation with Chen–Lee–Liu equation by traveling wave hypothesis and semi-inverse variational principle , 2018, Optik.

[31]  M. Akbar,et al.  Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method , 2017 .

[32]  Yongshuai Zhang,et al.  The soliton solutions for the Wadati-Konno-Ichikawa equation , 2020, Appl. Math. Lett..

[33]  A. Bekir,et al.  Analytic treatment of nonlinear evolution equations using first integral method , 2012 .

[34]  H. Rezazadeh,et al.  Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method , 2020, Physica Scripta.

[35]  N. Kudryashov.  Mathematical model of propagation pulse in optical fiber with power nonlinearities , 2020 .

[36]  Nikolai A. Kudryashov,et al.  Solitary wave solutions of hierarchy with non-local nonlinearity , 2020, Appl. Math. Lett..

[37]  M. Khan,et al.  The Modified Simple Equation Method and Its Application to Solve NLEEs Associated with Engineering Problem , 2015 .

[38]  Jian‐Guo Liu,et al.  Different wave structures and stability analysis for the generalized (2+1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation , 2020, Physica Scripta.

[39]  N. Kudryashov.  First integrals and solutions of the traveling wave reduction for the Triki–Biswas equation , 2019, Optik.

[40]  N. Kudryashov.  A generalized model for description of propagation pulses in optical fiber , 2019, Optik.

[41]  H. M. Baskonus,et al.  New acoustic wave behaviors to the Davey–Stewartson equation with power-law nonlinearity arising in fluid dynamics , 2016 .

[42]  Aly R. Seadawy,et al.  Construction of soliton solutions for modified Kawahara equation arising in shallow water waves using novel techniques , 2020 .

[43]  Saeid Abbasbandy,et al.  The first integral method for modified Benjamin–Bona–Mahony equation , 2010 .

[44]  Hasan Bulut,et al.  New Complex Hyperbolic Structures to the Lonngren-Wave Equation by Using Sine-Gordon Expansion Method , 2019, Applied Mathematics and Nonlinear Sciences.

[45]  M. Akbar,et al.  Closed form solutions of two time fractional nonlinear wave equations , 2018, Results in Physics.

[46]  Reza Abazari,et al.  Application of (G'/G)-expansion method to Regularized Long Wave (RLW) equation , 2011, Comput. Math. Appl..

[47]  N. Kudryashov.  General solution of traveling wave reduction for the Kundu–Mukherjee–Naskar model , 2019, Optik.

[48]  A. M. Rahman,et al.  Solitary wave solutions in plasma physics and acoustic gravity waves of some nonlinear evolution equations through enhanced MSE method , 2019, Journal of Physics Communications.

[49]  M. Belić,et al.  Optical solitons pertutabation with Fokas-Lenells equation by exp(−ϕ(ξ))-expansion method , 2019, Optik.

[50]  M. Osman,et al.  New optical solitary wave solutions of Fokas-Lenells equation in presence of perturbation terms by a novel approach , 2018, Optik.

[51]  Nikolai A. Kudryashov,et al.  Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations , 2020, Appl. Math. Comput..

[52]  M. Barakat,et al.  General improved Kudryashov method for exact solutions of nonlinear evolution equations in mathematical physics , 2020, Physica Scripta.

[53]  Rubayyi T. Alqahtani,et al.  Optical solitons with differential group delay for coupled Fokas–Lenells equation by extended trial function scheme , 2018, Optik.