The Solitary Wave Solutions for the Nonlinear Benjamin-Mahony Equation
Keywords:
Benjamin-Bona-Mahony; Riccati-Bernoulli sub-ODE method; water waves; Solitary wave.Abstract
The Benjamin-Bona-Mahony (BBM) equation is a nonlinear partial differential equation that describes the propagation of long waves in a shallow water channel. In this work, we present a comprehensive solution for the BBM equation using the Riccati-Bernoulli sub-ODE method. The method involves transforming the BBM equation into a Riccati equation, which is then further transformed into a Bernoulli equation. The Bernoulli equation is then solved analytically, and the solution is used to obtain the solution for the original BBM equation. Our results show that the Riccati-Bernoulli sub-ODE method provides an efficient
and accurate solution for the BBM equation. The method can be extended to solve other nonlinear partial differential equations (NPDEs), making it a valuable tool for researchers in various fields.
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