Soliton Solution of Benjamin-Bona-Mahony Equation and Modified Regularized Long Wave Equation

This article discusses about solutions of Benjamin-Bona-Mahony (BBM) equation and Modified Regularized Long Wave (MRLW) equation. BBM equation is a model describing the propagation of long wave with small amplitude on one directional space. This equation was developed to resolve the shortcoming of classic Korteweg-de-Vries (KdV) equation which fails to model the wave when the wavenumbers value is high. Meanwhile, MRLW equation represents the dispersed wave phenomenon such as shallow water and phonon packet on nonlinear crystal. The solutions of these equations are known as a solitary wave (soliton). This solution can be determined by various methods. Here, we apply the sine-cosine function method and analyze in detail the resulting solitary waves.