The investigation of a two-layer fluid soliton pair using phase plane analysis

Nonlinear long waves theory in a two-layer fluid system has been studied. The dynamical equations according to the normalized heights in first order are obtained using the reductive perturbation, method and the equations of shallow water in each fluid and taking boundary conditions appropriate into account Conserve energy form by definition a independent variable is found. By definition a Ljapunov function, the condition for stability are shown. A newtechnique was used to prove stability as well as existence of soliton pair using phase plane analysis.