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Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with p-power nonlinearities in two dimensions. (arXiv:1710.02739v1 [math-ph])
来源于:arXiv
Nonlinear generalizations of integrable equations in one dimension, such as
the KdV and Boussinesq equations with $p$-power nonlinearities, arise in many
physical applications and are interesting in analysis due to critical
behaviour. This paper studies analogous nonlinear $p$-power generalizations of
the integrable KP equation and the Boussinesq equation in two dimensions.
Several results are obtained. First, for all $p\neq 0$, a Hamiltonian
formulation of both generalized equations is given. Second, all Lie symmetries
are derived, including any that exist for special powers $p\neq0$. Third,
Noether's theorem is applied to obtain the conservation laws arising from the
Lie symmetries that are variational. Finally, explicit line soliton solutions
are derived for all powers $p>0$, and some of their properties are discussed. 查看全文>>