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,
ϕ
xt
+
ϕ
xxxz
/4+
ϕ
x
ϕ
xz
+
ϕ
xx
ϕ
z
/2+
∂
−1
x
ϕ
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.