Coupled KdV Equation With Self-consistent Sources And Its Solutions

The researchers are focus on coupled equations and equations with self-consistent sources in recent years. The two types of equations are widely used in physics, many models with two parts of different types could be expressed by coupled equations, and much interaction of two objects of different types could be expressed by equations with self-consistent sources. The equations of new type called coupled equations with self-consistent sources combining the equations of the two types would be interesting.The equations with self-consistent sources could be solved by using binary Darboux transformation with an arbitary function, and the coupled equations could be solved via solving the complex equations derived from the coupled equations. Combining the solving methods of the equations of the two types, this paper offers a method to construct the coupled KdV equation with self-consistent sources and a method to solve it. The negaton, positon and complexiton are showed in this paper too.