N-Soliton Solutions to a New (2 + 1) Dimensional Integrable Equation

Abstract

We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation, ${\varphi }_{xt}+{\varphi }_{xxxz}/4+{\varphi }_x{\varphi }_{xz}+{\varphi }_{xx}{\varphi }_z/2+{\partial }_x^{-1}{\varphi }_{zzz}/4=0$. This equation is obtained by unifying two directional generalization of the KdV equation, composing the closed ring with the KP equation and Bogoyavlenskii-Schiff equation. We also find the Miura transformation which yields the same ring in the corresponding modified equations.

7 pages, uses ioplppt.sty

References in corpus (2)

• Multilinear Operators: The Natural Extension Of Hirota's Bilinear Formalism
• Integrable Trilinear PDE's

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