Abstract
Four M-component nonlinear evolution equations, namely the M-component Korteweg–de Vries (KdV) equation, the M-component Kadomtsev–Petviashvili (KP) equation, the M-component modified KdV (mKdV) equation and the M-component mKdV–KP equation, are examined for complete integrability. The study relies mainly on the simplified form of Hirota's direct method developed by Hereman and on computer symbolic computation. Multiple soliton solutions and multiple singular soliton solutions are derived for each vector equation.
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