@misc{10498/33282,
year = {2018},
url = {http://hdl.handle.net/10498/33282},
abstract = {Nonlinear generalizations of integrable equations in one dimension, such as the Korteweg–de Vries and
Boussinesq equations with p-power nonlinearities, arise in many physical applications and are interesting
from the analytic standpoint because of their critical behavior. We study analogous nonlinear p-power
generalizations of the integrable Kadomtsev–Petviashvili and Boussinesq equations in two dimensions.
For all p <>0, we present a Hamiltonian formulation of these two generalized equations. We derive all
Lie symmetries including those that exist for special powers p <> 0. We use Noether’s theorem to obtain
conservation laws arising from the variational Lie symmetries. Finally, we obtain explicit line soliton
solutions for all powers p > 0 and discuss some of their properties},
publisher = {Springer},
keywords = {line soliton},
keywords = {conservation law},
keywords = {Kadomtsev–Petviashvili equation},
title = {Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with p-power nonlinearities in two dimensions},
doi = {10.1134/S004057791810001X},
author = {Anco, Stephen C. and Gandarias Núñez, María Luz and Recio Rodríguez, Elena},
}