Geodesic
Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with $p$-power nonlinearities in two dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 1, pp. 3-23

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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 $p\ne0$, we present a Hamiltonian formulation of these two generalized equations. We derive all Lie symmetries including those that exist for special powers $p\ne0$. 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.
Mots-clés : line soliton
Keywords: conservation law, Kadomtsev–Petviashvili equation. 
@article{TMF_2018_197_1_a0,
     author = {S. C. Anco and M. L. Gandarias and E. Recio},
     title = {Conservation laws, symmetries, and line soliton solutions of generalized {KP} and {Boussinesq} equations with $p$-power nonlinearities in two dimensions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--23},
     publisher = {mathdoc},
     volume = {197},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_1_a0/}
}
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S. C. Anco; M. L. Gandarias; E. Recio. Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with $p$-power nonlinearities in two dimensions. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 1, pp. 3-23. http://geodesic.mathdoc.fr/item/TMF_2018_197_1_a0/