The interaction of the ω-soflton and ω-cuspon of the Camassa-Holm equation

In this letter, we use the newly available explicit multi-soliton and multi-cuspon solutions of the Camassa-Holm equation to study the interactions of a soliton and a cuspon, two cuspons and two solitons. Some interesting phenomena are found, e.g., a larger soliton can 'eat up' a smaller cuspon during the collison and it is the other way round if the amplitude of the cuspon is larger. It is also found that a soliton and a cuspon can emerge from an almost zero mass. The interaction of two cuspons is also investigated in detail for the first time.