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.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 197, No. 1, pp. 3–23, October, 2018.
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Anco, S.C., Gandarias, M.L. & Recio, E. Conservation Laws, Symmetries, and Line Soliton Solutions of Generalized KP and Boussinesq Equations with p-Power Nonlinearities in Two Dimensions. Theor Math Phys 197, 1393–1411 (2018). https://doi.org/10.1134/S004057791810001X
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DOI: https://doi.org/10.1134/S004057791810001X