Champion soliton emergence from bipolar solitary wave interactions in the Schamel equation

Physics Letters A. 2026. Vol. 598. Article 132218.

Flamarion M., Didenkulova E., Pelinovsky E.

In this letter, bipolar solitary wave interactions in the Schamel equation are revisited numerically. Two simulation settings are considered: repeated collisions in a periodic domain, and the interaction of a positive solitary wave with a train of negative polarity solitary waves of equal amplitude. In the first case, when the amplitudes are comparable, the larger wave gains amplitude at the expense of the smaller one, and a tendency toward the formation of a champion soliton is observed. In the second case, a similar transfer occurs, but the positive wave also undergoes phase shifts and a soliton trajectory bending. It is further shown that a large sequence of collisions leads to a progressive increase in the amplitude of the larger solitary wave, reinforcing the tendency toward the formation of a champion soliton.

Keywords: солитон, soliton, Soliton turbulence, солитонная турбулентность, Schamel equation, уравнение Шамеля, Champion soliton, солитон-чемпион