<b><i>N</i></b>-soliton solutions to a -dimensional integrable equation

Song-Ju Yu, Kouichi Toda, Takeshi Fukuyama

Type: Article

Publication Date: 1998-12-18

Citations: 51

DOI: https://doi.org/10.1088/0305-4470/31/50/013

Abstract

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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Journal of Physics A Mathematical and General - View
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Works Cited by This (10)

Action	Title	Year	Authors
+	Spectral Transform and Solitons	1983	F. Calogero
+	Integrable Trilinear PDE's	1994	Jarmo Hietarinta B. Grammaticos A. Ramani
+	<b><i>N</i></b>soliton solutions to the Bogoyavlenskii-Schiff equation and a quest for the soliton solution in (3 1) dimensions	1998	Song-Ju Yu Kouichi Toda Narimasa Sasa Takeshi Fukuyama
+	On the gauge-invariant description of the evolution equations integrable by Gelfand-Dikij spectral problems	1982	B. G. Konopelchenko
+	A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I	1975	В. Е. Захаров A. B. Shabat
+	A method to generate solvable nonlinear evolution equations	1975	F. Calogero
+	The Painlevé property for partial differential equations	1983	John Weiss M. Tabor G. F. Carnevale
+	OVERTURNING SOLITONS IN NEW TWO-DIMENSIONAL INTEGRABLE EQUATIONS	1990	O I Bogoyavlenskiĭ
+	BREAKING SOLITONS. III	1991	O I Bogoyavlenskiĭ
+ PDF Chat	Multilinear operators: the natural extension of Hirota's bilinear formalism	1994	B. Grammaticos A. Ramani Jarmo Hietarinta