Abstract
The \bar∂-dressing method is extended to noncommutative space-time. It is shown that a noncommutative soliton equation and its Lax operators can be represented in the forms of Moyal product, the operator (functional of creation–annihilation operators) and the kernel function of the operator in coherent state representation (CSR). Noncommutative KP (ncKP) equation is taken as an example to illustrate how to solve a noncommutative soliton equation. It is found that the induced soliton equation in the CSR is different from the matrix KP equation usually considered in articles, but is a new soliton equation of integral operator. It is shown that the solutions of a noncommutative soliton equation (both multi-lump and multi-line solitons) can be reduced to solving a set of c -number linear differential equations.
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