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

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

1998-03-18

arxiv.org/abs/solv-int/9803012v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

7 pages, uses ioplppt.sty

Scientific paper

10.1088/0305-4470/31/50/013

We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation, $\phi_{xt} + \phi_{xxxz}/4 + \phi_x \phi_{xz} + \phi_{xx} \phi_z/2 + \partial_x^{-1} \phi_{zzz}/4 = 0$. 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.

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