Abstract
We apply the ∂¯-dressing method to study nonlocal modified Korteweg-de Vries (nonlocal mKdV) equation. A spatial and a time singular spectral problems associated with nonlocal mKdV equation are derived from a local 2×2 matrix ∂¯-equation via two linear constraint equations. A nonlocal mKdV hierarchy is proposed by using recursive operator. And the conservation laws of the nonlocal mKdV are derived by the temporal linear spectral problem. The N-solitions of the nonlocal mKdV equation are constructed still based the ∂¯-equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained. The results on the mKdV equation can be recovered from the conclusion given above as special reductions.
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