RT journal article
T1 Line-solitons, line-shocks, and conservation laws of a universal KP-like equation in 2+1 dimensions
A1 Anco, Stephen C.
A1 Gandarias Núñez, María Luz
A1 Recio Rodríguez, Elena
A2 Matemáticas
K1 Nonlinear wave
K1 Line soliton
K1 Line shock
K1 Conserved integral
K1 Physical parameterization
K1 Integral constraints
AB A universal KP-like equation in 2+1 dimensions, which models general nonlinear wave phenomena exhibiting p-power nonlinearity, dispersion, and small transver-sality, is studied. Special cases include the integrable KP (Kadomtsev-Petviashvili) equation and its modified version, as well as their p-power generalizations. Two main results are obtained. First, all low-order conservation laws are derived, includ-ing ones that arise for special powers p. The conservation laws comprise momenta, energy, and Galilean-type quantities, as well as topological charges. Their physical meaning and properties are discussed. The topological charges are shown to give rise to integral constraints on initial data for the Cauchy problem. Second, all line-soliton solutions are obtained in an explicit form. A parameterization is given using the speed and the direction angle of the line-soliton, and the allowed kinematic region is determined in terms of these parameters. Basic kinematical properties of the line-solitons are also discussed. These properties differ significantly compared to those for KP line-solitons and their p-power generalizations. A line-shock solution is shown to emerge when a special limiting case of the kinematic region is considered.
PB Elsevier
SN 0022-247X
YR 2021
FD 2021
LK http://hdl.handle.net/10498/33244
UL http://hdl.handle.net/10498/33244
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026