Abstract
This article’s purpose is to investigate the inverse scattering transform of the nonlocal long wave-short wave (LW-SW) equation and its multi-soliton solutions via Riemann-Hilbert (RH) approach. By using spectral analysis to the Lax pair of LW-SW equation, the RH problem can be constructed. However, we consider spectral analysis from the time part rather than the usual space part, since it is hard to obtain the analyticity of the space part. Then the RH problem can be solved and the formula of the soliton solutions can be given. We provide several special soliton solutions including Y-shaped solitons, V-shaped solitons, bound-state solitons and mixed four-soliton solutions. Compared with the local case, the solutions of nonlocal LW-SW equation exhibit distinct characteristics that (i) these soliton solutions are strictly symmetric with respect to x = 0 under special parameter conditions, (ii) the mixed four-soliton solution, which combines Y-type and bound-state solitons, is novel.
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