Physical properties for bidirectional wave solutions to a generalized fifth-order equation with third-order time-dispersion term

Abstract Higher-order temporal-dispersion partial differential equations have its capability to visualize the evolution of steeper-waves for shorter wave-length better than the higher-order KdV does. In this work, we study the physical-structure propagations of generalized fifth-order nonlinear equation involving time-dispersion term. This model is recently proposed by Wazwaz (Xu and Wazwaz, 2020) and is considered to be the first type of integrable equations that involves a third-order time-dispersion term. We implement three functional-methods to seek solitary wave solutions to the proposed model. 2D-plots are provided to recognize the type of the obtained solutions. Finally, we propose some physical properties of the bidirectional waves that such model admits.

[1]  K. Lamb,et al.  The Evolution of Internal Wave Undular Bores: Comparisons of a Fully Nonlinear Numerical Model with Weakly Nonlinear Theory , 1996 .

[2]  M. Alquran,et al.  A two-mode coupled Korteweg–de Vries: multiple-soliton solutions and other exact solutions , 2017 .

[3]  S. Momani,et al.  Development of spreading symmetric two-waves motion for a family of two-mode nonlinear equations , 2020, Heliyon.

[4]  Imad Jaradat,et al.  Construction of Solitary Two-Wave Solutions for a New Two-Mode Version of the Zakharov-Kuznetsov Equation , 2020, Mathematics.

[5]  Ebru Cavlak Aslan,et al.  Soliton solutions of NLSE with quadratic-cubic nonlinearity and stability analysis , 2017 .

[6]  Xi-Qiang Liu,et al.  Symmetry reduction, exact solutions and conservation laws of a new fifth-order nonlinear integrable equation , 2013, Commun. Nonlinear Sci. Numer. Simul..

[7]  F. Tchier,et al.  Dynamics of solitons to the ill-posed Boussinesq equation , 2017 .

[8]  Mohammed Ali,et al.  A numerical study on weak-dissipative two-mode perturbed Burgers’ and Ostrovsky models: right-left moving waves , 2018 .

[9]  F. Tchier,et al.  Optical solitons of the coupled nonlinear Schrödinger’s equation with spatiotemporal dispersion , 2016 .

[10]  D. Baleanu,et al.  Shapes and dynamics of dual-mode Hirota–Satsuma coupled KdV equations: Exact traveling wave solutions and analysis , 2019, Chinese Journal of Physics.

[11]  Jian‐Guo Liu,et al.  Exact periodic cross-kink wave solutions for the (2+1)-dimensional Korteweg-de Vries equation , 2020 .

[12]  M. Alquran,et al.  Reliable study of some new fifth-order nonlinear equations by means of G'/G expansion method and rational sine-cosine method , 2014 .

[13]  G. Akram,et al.  Exact solitary wave solutions by extended rational sine-cosine and extended rational sinh-cosh techniques , 2019, Physica Scripta.

[14]  A. Wazwaz.  A new generalized fifth-order nonlinear integrable equation , 2011 .

[15]  M. Alquran,et al.  A study on the two-mode coupled modified Korteweg–de Vries using the simplified bilinear and the trigonometric-function methods , 2017 .

[16]  Mohammed Ali,et al.  Changes in the physical structures for new versions of the Degasperis-Procesi-Camassa-Holm model , 2020 .

[17]  Chun-Ku Kuo.  Resonant multi-soliton solutions to two fifth-order KdV equations via the simplified linear superposition principle , 2019, Modern Physics Letters B.

[18]  M. Alquran,et al.  Dynamism of two-mode’s parameters on the field function for third-order dispersive Fisher: application for fibre optics , 2018, Optical and Quantum Electronics.

[19]  Jian‐Guo Liu,et al.  Multiple rogue wave, breather wave and interaction solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation , 2021, Nonlinear Dynamics.

[20]  M. Inç,et al.  Compact and non compact structures of the phi-four equation , 2017 .

[21]  Wenxiu Ma,et al.  A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation , 2009, 0903.5337.

[22]  Zhenya Yan,et al.  The new tri-function method to multiple exact solutions of nonlinear wave equations , 2008 .

[23]  Jian‐Guo Liu,et al.  Stripe solitons and lump solutions to a generalized (3 + 1)-dimensional B-type Kadomtsev-Petviashvili equation with variable coefficients in fluid dynamics , 2019, 1911.07230.

[24]  F. Tchier,et al.  On optical solitons of the Schrödinger-Hirota equation with power law nonlinearity in optical fibers , 2017 .

[25]  Abdul-Majid Wazwaz,et al.  Kink solutions for three new fifth order nonlinear equations , 2014 .

[26]  A. Yusuf,et al.  Kink-soliton, singular-kink-soliton and singular-periodic solutions for a new two-mode version of the Burger–Huxley model: applications in nerve fibers and liquid crystals , 2021, Optical and Quantum Electronics.

[27]  Yavuz Ugurlu,et al.  New applications of the functional variable method , 2017 .

[28]  Marwan Alquran,et al.  Dual-wave solutions for the quadratic-cubic conformable-Caputo time-fractional Klein-Fock-Gordon equation , 2021, Math. Comput. Simul..

[29]  Nikolai A. Kudryashov,et al.  One method for finding exact solutions of nonlinear differential equations , 2011, 1108.3288.

[30]  A. Wazwaz.  A new fifth-order nonlinear integrable equation: multiple soliton solutions , 2011 .

[31]  Abdullahi Yusuf,et al.  Optical and other solitons for the fourth-order dispersive nonlinear Schrödinger equation with dual-power law nonlinearity , 2017 .

[32]  A. Yusuf,et al.  Heart-cusp and bell-shaped-cusp optical solitons for an extended two-mode version of the complex Hirota model: application in optics , 2021 .

[33]  M. Alquran,et al.  A modified approach for a reliable study of new nonlinear equation: two-mode Korteweg–de Vries–Burgers equation , 2018 .

[34]  Jian‐Guo Liu,et al.  New three-wave solutions for the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation , 2017 .

[35]  I. Sagnes,et al.  Third Order Dispersion in Time-Delayed Systems. , 2019, Physical review letters.

[36]  Jian-Guo Liu,et al.  Abundant lump and lump–kink solutions for the new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation , 2018 .

[37]  A. Wazwaz,et al.  Bidirectional solitons and interaction solutions for a new integrable fifth-order nonlinear equation with temporal and spatial dispersion , 2020, Nonlinear Dynamics.