Solutions to Benjamin-Bona-Mahony Equation in Two Space Dimensions by Various Methods

Alper Korkmaz

doi:10.20944/preprints201807.0575.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 29 July 2018 / Approved: 30 July 2018 / Online: 30 July 2018 (10:00:20 CEST)

Four methods in two different families have been constructed to derive the exact solutions to Benjamin-Bona-Mahony equation in two space dimensions. Simply defined hyperbolic tangent, hyperbolic secant and hyperbolic cosecant ansatzes and the expansion method based on the Sine-Gordon equation in two dimensions are directly substituted into the governing ODE reduced from the two dimensional BBM equation. Classical algebraic method is used to find the relations among the target parameters representing the nonzero coefficients in the predicted solutions and the wave transform parameters. Some complex and real solutions have been constructed in explicit forms.

2D RLW equation; 2D BBM equation; ansatz; series expansion method based on Sine-Gordon equation; traveling wave solution

Computer Science and Mathematics, Mathematics

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Solutions to Benjamin-Bona-Mahony Equation in Two Space Dimensions by Various Methods

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