Exact solutions with compact and noncompact structures for the one-dimensional generalized Benjamin–Bona–Mahony equation |
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Authors: | Abdul-Majid Wazwaz |
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Institution: | Department of Mathematics and Computer Science, Saint Xavier University, 3700 West 103rd Street, Chicago, IL 60655, USA |
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Abstract: | This paper is devoted to analyzing the physical structures of nonlinear dispersive variants of the Benjamin–Bona–Mahony equation. It is found that these generalized forms give rise to compactons solutions: solitons with the absence of infinite tails, solitons: nonlinear localized waves of infinite support, solitary patterns solutions having infinite slopes or cusps, and plane periodic solutions. It is also found that the qualitative change in the physical structure of solutions depends strongly on whether the exponents of the wave function u(x, t) whether it is positive or negative, and on the speed c of the traveling wave as well. |
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Keywords: | Compactons Solitons Solitary patterns solutions Periodic solutions Benjamin– Bona– Mahony equation Sine– cosine ansatz |
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