On the Structure During Interaction of the Two-Soliton Solution of the Korteweg–de Vries Equation

By analysing the structure during interaction of the soliton elements in the two-soliton solution of the Korteweg–de Vries equation, it is shown how to calculate the duration of the interaction for two soliton elements with any amplitude ratio. It is also clarified that the soliton elements (as defined here) always pass through one another irrespective of the magnitude of the amplitude ratio of the soliton elements. This conclusion confirms most previous reports on the interaction of the soliton elements but contradicts another report which states that when amplitudes of the soliton elements are nearly equal, the soliton elements do not pass through each other but rather advance toward each other, bounce off one another, and then recede from each other. However, it should be noted that in the last case the definition of the soliton elements is different from that given here.