The integrability of coupled KdV equations is examined. The simplified form of Hirota’s bilinear method is used to achieve this goal. Multiple-soliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation. The resonance phenomenon of each model will be examined.
In this work, two new completely integrable extensions of the Kadomtsev-Petviashvili (eKP) equation are developed. Multiple soliton solutions and multiple singular soliton solutions are derived to demonstrate the compatibility of the extensions of the KP equation.
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