The bright $N$-soliton solution of a multi-component modified nonlinear Schrödinger equation

Details The bright $N$-soliton solution of a multi-component modified nonlinear Schrödinger equation The bright $N$-soliton solution of a multi-component modified nonlinear Schrödinger equation

2011-10-25

arxiv.org/abs/1110.5421v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

To appear in J. Phys. A: Math. Theor

Scientific paper

A direct method is developed for constructing the bright $N$-soliton solution of a multi-component modified nonlinear Schr\"odinger equation. Specifically, the two different expressions of the solution are obtained both of which are expressed as a rational function of determinants. A simple relation is found between them by employing the properties of the Cauchy matrix. The proof of the solution reduces to the bilinear equations among the bordered determinants in which Jacobi's identity and related formulas play a central role. Last, the bright $N$-soliton solution is presented for a (2+1)-dimensional nonlocal model equation arising from the multi-component system as the number of dependent variables tends to infinity.

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