Abstract
We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the(G'/G)-expansion method.
Highlights
Many phenomena in the real world are often described by nonlinear evolution equations (NLEEs) and such equations play an important role in applied mathematics, physics, and engineering
By using Ibragimov theorem [24], the components of the conserved vector associated with the symmetry
We look for solutions of (14) and (15) in the form: ψ (z)
Summary
Many phenomena in the real world are often described by nonlinear evolution equations (NLEEs) and such equations play an important role in applied mathematics, physics, and engineering. In addition to exact solutions there is a need to find conservation laws for the NLEEs. Conservation laws assist in the numerical integration of partial differential equations [11], theory of nonclassical transformations [12, 13], normal forms, and asymptotic integrability [14]. Conservation laws have been used to derive exact solutions of partial differential equations [15,16,17]. Bifurcation method was used by Song and Yang [23] to obtain exact solitary wave solutions and kink wave solutions. Conservation laws will be derived for (1) using the new conservation theorem due to Ibragimov [24] and the multiplier method [25]. The (G/G)expansion method [6] is used to obtain the traveling wave solutions for (1)
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