N-Soliton Solutions to a New (2 + 1) Dimensional Integrable Equation
S. J. Yu, K. Toda, T. Fukuyama
Abstract
We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation, ϕxt + ϕxxxz/4 + ϕx ϕxz + ϕxx ϕz/2 + ∂x-1 ϕzzz/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.
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