Nonlinearly dispersive KP equations with new compacton solutions
Abstract
A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher spatial dimensions. In particular, precise conditions are given on the nonlinearity powers in this equation under which a travelling wave can be cut off to obtain a compacton. Numerous explicit examples having various profiles are derived, including a quadratic function, powers of a cosine, and powers of Jacobi functions, all of which are symmetric. The cosine and symmetric compactons have an anti-symmetric counterpart. In comparison, explicit solitary waves of the generalized KP equation are found to have profiles given by a power of a sech and a reciprocal quadratic function. Kinematic properties of all of the different types of compactons and solitary waves are discussed, along with conservation laws of the generalized KP equation.
Cite
@article{arxiv.2103.15251,
title = {Nonlinearly dispersive KP equations with new compacton solutions},
author = {Stephen C. Anco and Maria Gandarias},
journal= {arXiv preprint arXiv:2103.15251},
year = {2025}
}
Comments
27 pages; 12 figures. Cutoff conditions have been clarified; details added to proof of Theorem 5.1; highlights of compactons for linear dispersion have been added; more discussion of kinematic features of all compacton. Published version