Applied Mathematics & Information Sciences

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New solitary solutions of some nonlinear partial differential equations are constructed using the generalized Bernoulli method. The main idea of this method is to make use of Bernoulli differential equation which has a simple exponential solution. The ZK-BBM (Zakharov-Kuznetsov-Benjamin–Bona–Mahony), a nonlinear dispersive, and the general Burgers-Fisher equations are solved and numerically investigated. The ZK equation that describes two-dimensional, magnetized, collisionless pair ions plasma is also presented as a problem of physical interest. Comparisons with G’/G-expansion method are given for the sake of assessments of Bernoulli method. Successfully, this method not only gives new solitary solutions of the problems under consideration but also recovers some solutions that had been obtained by other methods for the same problems.

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