Advances in solving conformable nonlinear partial differential equations and new exact wave solutions for Oskolkov‐type equations

2021 ◽  
Author(s):  
Hayman Thabet ◽  
Subhash Kendre ◽  
James Peters
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Wave Solutions

scholarly journals Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2-Expansion Method

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Rational Solutions ◽  
Partial Differential ◽  
Wave Solutions

We apply the G′/G2-expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigonometric solutions, exponential solutions, and rational solutions. The applications of the method are simple, efficient, and reliable by means of using a symbolically computational package. Applying the proposed method to the problems, we have some innovative exact solutions which are different from the ones obtained using other methods employed previously.

Exact Travelling Wave Solutions of two Important Nonlinear Partial Differential Equations

2014 ◽  
Vol 69 (3-4) ◽  
pp. 155-162 ◽  
Author(s):  
Hyunsoo Kim ◽  
Jae-Hyeong Bae ◽  
Rathinasamy Sakthivel
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Temporal Dynamics ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Kudryashov Method

Coupled nonlinear partial differential equations describing the spatio-temporal dynamics of predator-prey systems and nonlinear telegraph equations have been widely applied in many real world problems. So, finding exact solutions of such equations is very helpful in the theories and numerical studies. In this paper, the Kudryashov method is implemented to obtain exact travelling wave solutions of such physical models. Further, graphic illustrations in two and three dimensional plots of some of the obtained solutions are also given to predict their behaviour. The results reveal that the Kudryashov method is very simple, reliable, and effective, and can be used for finding exact solution of many other nonlinear evolution equations.

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