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  1. 2 Open Physics

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  1. 2 2013

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  1. 2 Wazwaz A.-M.

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Multiple soliton solutions for the integrable couplings of the KdV and the KP equations

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Wazwaz A.-M.
Open Physics
|
2013
|
vol. 11
|
issue 3
291-295
EN
In this work, we study the nonlinear integrable couplings of the KdV and the Kadomtsev-Petviashvili (KP) equations. The simplified Hirota’s method will be used for this study. We show that these couplings possess multiple soliton solutions the same as the multiple soliton solutions of the KdV and the KP equations, but differ only in the coefficients of the transformation used. This difference exhibits soliton solutions for some equations and anti-soliton solutions for others.
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An eighth-order KdV-type equation in (1+1) and (2+1) dimensions: multiple soliton solutions

80%
Wazwaz A.-M.
Open Physics
|
2013
|
vol. 11
|
issue 1
143-146
EN
In this work we study an eighth-order KdV-type equations in (1+1) and (2+1) dimensions. The new equations are derived from the KdV6 hierarchy. We show that these equations give multiple soliton solutions the same as the multiple soliton solutions of the KdV6 hierarchy except for the dispersion relations.
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