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

S. J. Yu; K. Toda; T. Fukuyama

doi:10.1088/0305-4470/31/50/013

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arXiv · solv-int/9803012

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

S. J. Yu·K. Toda·T. Fukuyama

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Abstract

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

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BibTeX RIS

S. J. Yu, K. Toda, T. Fukuyama. 1998-03-18. N-Soliton Solutions to a New (2 + 1) Dimensional Integrable Equation. https://doi.org/10.1088/0305-4470%2F31%2F50%2F013

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