Using
commutation methods, the
authors present a
general formalism to
construct Korteweg-de Vries (KdV) and
modified Korteweg-de Vries (mKdV) $N$-soliton solutions relative to arbitrary (m)KdV background solutions. As an illustration of these techniques, the authors combine them with algebro-geometric methods and Hirota's $\tau$-function approach to systematically derive the (m)KdV $N$-soliton solutions on quasi-periodic finite-gap backgrounds..
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