%0 Journal Article 
%A Anco, Stephen C.
%A Gandarias Núñez, María Luz
%A Recio Rodríguez, Elena
%T Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with p-power nonlinearities in two dimensions
%D 2018
%@ 0040-5779
%U http://hdl.handle.net/10498/33282
%X 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
%K line soliton
%K conservation law
%K Kadomtsev–Petviashvili equation
%~ Universidad de Cádiz