Weak compactons of nonlinearly dispersive KdV and KP equations
Mathematical Physics
2025-02-06 v2 math.MP
Abstract
A weak formulation is devised for the K(m,n) equation which is a nonlinearly dispersive generalization of the gKdV equation having compacton solutions. With this formulation, explicit weak compacton solutions are derived, including ones that do not exist as classical (strong) solutions. Similar results are obtained for a nonlinearly dispersive generalization of the gKP equation in two dimensions, which possesses line compacton solutions.
Keywords
Cite
@article{arxiv.2401.00938,
title = {Weak compactons of nonlinearly dispersive KdV and KP equations},
author = {Stephen C. Anco and Maria Gandarias},
journal= {arXiv preprint arXiv:2401.00938},
year = {2025}
}
Comments
17 pages, published version