Insight into Functional Boiti–Leon–Mana–Pempinelli Equation and Error Control: Approximate Similarity Solutions

Manal Alqhtani, Rekha Srivastava, Hamdy I. Abdel-Gawad, Jorge E. Macías-Díaz (), Khaled M. Saad and Waleed M. Hamanah
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Manal Alqhtani: Department of Mathematics, College of Sciences and Arts, Najran University, Najran 66262, Saudi Arabia
Rekha Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Hamdy I. Abdel-Gawad: Mathematics Department, Faculty of Science, Cairo University, Giza 12613, Egypt
Jorge E. Macías-Díaz: Department of Mathematics, School of Digital Technologies, Tallinn University, 10120 Tallinn, Estonia
Khaled M. Saad: Department of Mathematics, College of Sciences and Arts, Najran University, Najran 66262, Saudi Arabia
Waleed M. Hamanah: Applied Research Center for Metrology, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia

Mathematics, 2023, vol. 11, issue 22, 1-21

Abstract: The Boiti–Leon–Mana–Pempinelli Equation (BLMPE) is an essential mathematical model describing wave propagation in incompressible fluid dynamics. In the present manuscript, a novel generalization of the BLMPE is introduced, called herein the functional BLMPE (F-BLMPE), which involves different functions, including exponential, logarithmic and monomaniacal functions. In these cases, the F-BLMPE reduces to an explicit form in the dependent variable. In addition to this, it is worth deriving approximate similarity solutions of the F-BLMPE with constant coefficients using the extended unified method (EUM). In this method, nonlinear partial differential equation (NLPDE) solutions are expressed in polynomial and rational forms through an auxiliary function (AF) with adequate auxiliary equations. Exact solutions are estimated using formal solutions substituted into the NLPDEs, and the coefficients of the AF of all powers are set equal to zero. This approach is valid when the NLPDE is integrable. However, this technique is not valid for non-integrable equations, and only approximate solutions can be found. The maximum error can be controlled by an adequate choice of the parameters in the residue terms (RTs). Multiple similarity solutions are derived, and the ME is depicted in various examples within this work. The results found here confirm that the EUM is an efficient method for solving NLPDEs of the F-BLMPE type.

Keywords: functional equation; Boiti–Leon–Mana–Pempinelli equation; similarity solutions; error control; unified method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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