Уравнение Олвера как альтернатива уравнению Кортевега—де Вриза

We study analytically and numerically the soliton solutions of the Olver equation, proposed in 1984 as an alternative to the KdV equation. The Olver equation is notable for its compliance with energy conservation consistent with the time invariance of physical laws. Olver demonstrated that, within the classical KdV equation, the conserved quantity associated with wave energy cannot be directly derived from the genuine wave energy of surface water waves in the small-amplitude, long-wave limit. Until now, soliton solutions to the Olver equation had not been obtained, nor had their properties been thoroughly studied. In this paper, we fill this gap by deriving such solutions and analyzing solitary wave interactions. Our results indicate that soliton interactions are inelastic, providing evidence that the Olver equation is non-integrable. However, no formation of a soliton-champion occurs in a closed system after numerous collisions between solitons of different amplitudes. Instead, a statistical equilibrium between the solitons and the radiated small-amplitude wave field onsets.