A note on the Sine-Gordon expansion method and its applications

The sine-Gordon expansion method; which is a transformation of the sine-Gordon equation has been applied to the potential-YTSF equation of dimension (3+1) and the reaction-diffusion equation. We obtain new solitons of this equation in the form hyperbolic, complex and trigonometric function by using this method. We plot 2D and 3D graphics of these solutions using symbolic software.

[1]  A. H. Khater,et al.  The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction-diffusion equations , 2002 .

[2]  Hong Zhao,et al.  Generalized method to construct the solitonic solutions to (3+1)-dimensional nonlinear equation , 2006 .

[3]  Abdul-Majid Wazwaz,et al.  Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method , 2006, Appl. Math. Comput..

[4]  M. A. Abdou,et al.  New explicit and exact traveling wave solutions for two nonlinear evolution equations , 2008 .

[5]  Khaled A. Gepreel,et al.  The (G′/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics , 2009 .

[6]  J. Manafian,et al.  Applications of He's semi-inverse method, ITEM and GGM to the Davey-Stewartson equation , 2017 .

[7]  D. Baleanu,et al.  A novel technique to construct exact solutions for nonlinear partial differential equations , 2019, The European Physical Journal Plus.

[8]  S. Y. Doka,et al.  Discrete exact solutions for the double-well potential model through the discrete tanh method , 2015 .

[9]  Integration of nonlinear system of four waves with two velocities in (2 + 1) dimensions by the inverse scattering transform method , 2011 .

[10]  Mingliang Wang,et al.  The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics , 2008 .

[11]  Ozlem Ersoy Hepson,et al.  Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class , 2020 .

[12]  H. M. Baskonus,et al.  On the new wave solutions to a nonlinear model arising in plasma physics , 2018 .

[13]  J. A. E. R. Institute,et al.  N soliton solutions to the Bogoyavlenskii-Schiff equation and a quest for the soliton solution in (3 1) dimensions , 1998, solv-int/9801003.

[14]  L. Debnath Solitons and the Inverse Scattering Transform , 2012 .

[15]  Abdul-Majid Wazwaz,et al.  New solutions of distinct physical structures to high-dimensional nonlinear evolution equations , 2008, Appl. Math. Comput..

[16]  M. El-Borai,et al.  Exact and soliton solutions to nonlinear transmission line model , 2017 .

[17]  H. M. Baskonus,et al.  Investigation of various travelling wave solutions to the extended (2+1)-dimensional quantum ZK equation , 2017 .

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

[19]  W. Malfliet Solitary wave solutions of nonlinear wave equations , 1992 .

[20]  Thierry Gallouët,et al.  Nonlinear Schrödinger evolution equations , 1980 .

[21]  Lena Vogler,et al.  The Direct Method In Soliton Theory , 2016 .

[22]  W. Schiesser,et al.  Sine-Gordon Equation , 2011 .

[23]  Hasan Bulut,et al.  Novel hyperbolic behaviors to some important models arising in quantum science , 2017 .

[24]  Zhenya Yan,et al.  New families of nontravelling wave solutions to a new (3+1)-dimensional potential-YTSF equation , 2003 .

[25]  E. Zayed,et al.  Solitons and other solutions to nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity using several different techniques , 2017 .

[26]  Elçin Yusufoglu,et al.  Symbolic computation and new families of exact travelling solutions for the Kawahara and modified Kawahara equations , 2008, Comput. Math. Appl..

[27]  Bo Tian,et al.  Generalized tanh method with symbolic computation and generalized shallow water wave equation , 1997 .

[28]  N. Kudryashov,et al.  Exact traveling soliton solutions for the generalized Benjamin-Bona-Mahony equation , 2018 .

[29]  M. Ablowitz,et al.  Nonlinear-evolution equations of physical significance , 1973 .

[30]  Mingliang Wang,et al.  Periodic wave solutions to a coupled KdV equations with variable coefficients , 2003 .

[31]  Abdul-Majid Wazwaz,et al.  The tan h method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations , 2005 .

[32]  Dipankar Kumar,et al.  The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics , 2017 .

[33]  Abdul-Majid Wazwaz,et al.  Traveling wave solutions of a (2 + 1)-dimensional Zakharov-like equation by the first integral method and the tanh method , 2016 .

[34]  H. M. Baskonus,et al.  Novel archetypes of new coupled Konno–Oono equation by using sine–Gordon expansion method , 2017 .

[35]  A. Scott,et al.  Solitons and the Inverse Scattering Transform (Mark J. Ablowitz and Harvey Segur) , 1983 .

[36]  R. Ansari,et al.  New exact traveling wave solutions of the Tzitzéica type equations using a novel exponential rational function method , 2017 .

[37]  Yi-Tian Gao,et al.  Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas , 2016 .

[38]  Chuntao Yan A simple transformation for nonlinear waves , 1996 .

[39]  Alwyn Scott Solitons and Nonlinear Wave Equations (R. K. Dodd, J. C. Eilbeck, J. D. Gibbon and H. C. Morris) , 1984 .