As one of the important physical models, the variable-coefficient breaking soliton model describes the dynamics of solitary waves and Riemann waves in hydrodynamics. Applying the two function approach into the variable-coefficient breaking soliton model, we find an exponential-form variable separation solution with two arbitrary functions, which covers many hyperbolic and trigonometric function solutions. Based on this solution and choosing suitably two arbitrary functions, complex waves including dromion pair and single dromion superposed on a line soliton background and their collisions between complex waves and between dromion and periodic wave are discussed. For the complex waves such as the dromion pair and single dromion superposed on a line soliton background and their collisions between complex waves, two components of this model possess both striking physical meanings. However, for the collision between dromion and periodic wave, one component of this model has unique physical meaning, yet the other component of the same model appears the singularity structure. Therefore, when one discusses complex waves and their collisions for one component of the model, one must take care of non-physical structures for another component of the same model lest one arbitrarily claims that he finds the so-called novel localized structures, which are actually false non-physical structures.

变系数破碎孤子模型作为重要的物理模型之一，描述了流体动力学中孤立波和黎曼波的动力学。将二函数方法应用到变系数破孤子模型中，我们找到了一个具有两个任意函数的指数形式的变量分离解，它涵盖了许多双曲函数和三角函数解。基于该解决方案并选择合适的两个任意功能，讨论了包括DROMION对的复杂波和叠加在孤子背景的单个DROMION及其在复杂波之间的碰撞和散发和周期波之间。对于叠加在线孤子背景上的dromion对和单dromion等复杂波及其复杂波之间的碰撞，该模型的两个组成部分都具有惊人的物理意义。然而，对于dromion和周期波的碰撞，该模型的一个分量具有独特的物理意义，而同一模型的另一个分量则出现奇点结构。因此，当一个人讨论模型的一个组件的复杂波及其碰撞时，必须注意同一模型的另一个组件的非物理结构，以免有人武断地声称他找到了所谓的新局域结构，即实际上是虚假的非物理结构。