Chaotic and fractal patterns for interacting nonlinear waves

Using an appropriate reduction method, a quite general new integrable system of equations 2 + 1 dimensions can be derived from the dispersive long-wave equation. Various soliton and dromion solutions are obtaining by selecting some types of solutions appropriately. The interaction between the localized solutions is completely elastic, because they pass through each other and preserve their shapes and velocities, the only change being a phase shift. The arbitrariness of the functions included in the general solution implies that approximate lower dimensional chaotic patterns such as chaotic–chaotic patterns, periodic–chaotic patterns, chaotic line soliton patterns and chaotic dromion patterns can appear in the solution. In a similar way, fractal dromion patterns and stochastic fractal excitations also exist for appropriate choices of the boundary conditions and/or initial conditions.