The collision of multimode dromions and a firewall in the two-component long-wave-short-wave resonance interaction equation. (English) Zbl 1163.35037

Summary: We investigate the two-component long-wave-short-wave resonance interaction equation and show that it admits the Painlevé property. We then suitably exploit the recently developed truncated Painlevé approach to generate exponentially localized solutions for the short-wave components \(S^{(1)}\) and \(S^{(2)}\) while the long wave \(L\) admits a line soliton only. The exponentially localized solutions driving the short waves \(S^{(1)}\) and \(S^{(2)}\) in the \(y\)-direction are endowed with different energies (intensities) and are called ’multimode dromions’. We also observe that the multimode dromions suffer from intramodal inelastic collision while the existence of a firewall across the modes prevents the switching of energy between the modes.


35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
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