RIEMANN–HILBERT APPROACH AND N -SOLITON SOLUTIONS OF THE GENERALIZED MIXED NONLINEAR SCHR ¨ODINGER EQUATION

We apply the Riemann–Hilbert method to the generalized mixed nonlinear Schr¨odinger equation and obtain a new formula for an explicit N -soliton solution, which is expressed as a ratio of ( N + 1) × ( N + 1) and N × N determinants. Using asymptotic analysis and the property of the Cauchy determinant, we derive simple elastic interactions of N -solitons.

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