Painlevé integrability and multi-wave pattern for (2+1)-dimensional long wave–short wave resonance interaction system

In this article, Painlevé analysis is employed to test the integrability of (2+1)-dimensional long wave–short wave resonance interaction system using the Weiss–Tabor–Carnevale method. From the analysis, it is seen that the long wave–short wave resonance interaction system satisfies Painlevé property and the system is expected to be integrable. Then, the long wave–short wave resonance interaction system is investigated by adopting the truncated Painlevé approach. The solutions are obtained in terms of arbitrary functions in the closed form. By selecting appropriate arbitrary functions present in the solutions, localized solutions such as rogue waves, lump, one-dromion and two-dromion wave patterns are constructed. The results are also expressed graphically to illustrate the physical behavior of the long wave–short wave resonance interaction system.