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Article

Variable Coefficient Exact Solutions for Some Nonlinear Conformable Partial Differential Equations Using an Auxiliary Equation Method

1
Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
2
Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
*
Author to whom correspondence should be addressed.
Academic Editors: Yongwimon Lenbury, Ravi P. Agarwal, Philip Broadbridge and Dongwoo Sheen
Received: 19 February 2021 / Revised: 6 March 2021 / Accepted: 7 March 2021 / Published: 10 March 2021
The objective of this present paper is to utilize an auxiliary equation method for constructing exact solutions associated with variable coefficient function forms for certain nonlinear partial differential equations (NPDEs) in the sense of the conformable derivative. Utilizing the specific fractional transformations, the conformable derivatives appearing in the original equation can be converted into integer order derivatives with respect to new variables. As for applications of the method, we particularly obtain variable coefficient exact solutions for the conformable time (2 + 1)-dimensional Kadomtsev–Petviashvili equation and the conformable space-time (2 + 1)-dimensional Boussinesq equation. As a result, the obtained exact solutions for the equations are solitary wave solutions including a soliton solitary wave solution and a bell-shaped solitary wave solution. The advantage of the used method beyond other existing methods is that it provides variable coefficient exact solutions covering constant coefficient ones. In consequence, the auxiliary equation method based on setting all coefficients of an exact solution as variable function forms can be more extensively used, straightforward and trustworthy for solving the conformable NPDEs. View Full-Text
Keywords: variable coefficient exact solutions; auxiliary equation method; conformable time (2 + 1)-dimensional Kadomtsev–Petviashvili equation; conformable space-time (2 + 1)-dimensional Boussinesq equation variable coefficient exact solutions; auxiliary equation method; conformable time (2 + 1)-dimensional Kadomtsev–Petviashvili equation; conformable space-time (2 + 1)-dimensional Boussinesq equation
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MDPI and ACS Style

Sirisubtawee, S.; Thamareerat, N.; Iatkliang, T. Variable Coefficient Exact Solutions for Some Nonlinear Conformable Partial Differential Equations Using an Auxiliary Equation Method. Computation 2021, 9, 31. https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030031

AMA Style

Sirisubtawee S, Thamareerat N, Iatkliang T. Variable Coefficient Exact Solutions for Some Nonlinear Conformable Partial Differential Equations Using an Auxiliary Equation Method. Computation. 2021; 9(3):31. https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030031

Chicago/Turabian Style

Sirisubtawee, Sekson, Nuntapon Thamareerat, and Thitthita Iatkliang. 2021. "Variable Coefficient Exact Solutions for Some Nonlinear Conformable Partial Differential Equations Using an Auxiliary Equation Method" Computation 9, no. 3: 31. https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030031

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