We consider the generalization of the customary Bäcklund transform (≡BT) for the two-dimensional (2D) KdV equation, (ut+6uux+uxxx)x +3α2uyy = 0, with α being constant. A nonlinear superposition formula has been obtained and it is shown that the present generalized BT can produce multiple soliton–multiple decay mode solutions.
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Akira Nakamura (1981) studied this question.
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