Perturbation theory for approximately integrable partial differential equations, and the change of amplitude of solitary-wave solutions of the BBM equation

1987 ◽  
Vol 182 (-1) ◽  
pp. 467 ◽  
Author(s):  
J. G. B. Byatt-Smith
Keyword(s):  
Perturbation Theory ◽  
Partial Differential Equations ◽  
Solitary Wave ◽  
Differential Equations ◽  
Solitary Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Bbm Equation

scholarly journals Some Applications of the (G′/G,1/G)-Expansion Method for Finding Exact Traveling Wave Solutions of Nonlinear Fractional Evolution Equations

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 952
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert ◽  
Surattana Sungnul
Keyword(s):  
Partial Differential Equations ◽  
Solitary Wave ◽  
Differential Equations ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Solitary Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions

In this paper, the ( G ′ / G , 1 / G ) -expansion method is applied to acquire some new, exact solutions of certain interesting, nonlinear, fractional-order partial differential equations arising in mathematical physics. The considered equations comprise the time-fractional, (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation, and the space-time-fractional generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) system in the sense of the conformable fractional derivative. Applying traveling wave transformations to the equations, we obtain the corresponding ordinary differential equations in which each of them provides a system of nonlinear algebraic equations when the method is used. As a result, many analytical exact solutions obtained of these equations are expressed in terms of hyperbolic function solutions, trigonometric function solutions, and rational function solutions. The graphical representations of some obtained solutions are demonstrated to better understand their physical features, including bell-shaped solitary wave solutions, singular soliton solutions, solitary wave solutions of kink type, and so on. The method is very efficient, powerful, and reliable for solving the proposed equations and other nonlinear fractional partial differential equations with the aid of a symbolic software package.

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