Experimental Evidence of Three–wave Zakharov–Manakov Solitons

Three–wave nonlinear resonant interaction (TWRI) is typically encountered in the description of any conservative nonlinear medium where the nonlinear dynamics can be considered as a perturbation of the linear wave solution, the lowest–order nonlinearity is quadratic in the field amplitudes, the three–wave resonance can be satisfied [1]. Indeed TWRI is the lowest–order nonlinear effect for a system approximately described by a linear superposition of discrete waves. TWRI has been extensively studied alongside with the development of plasma physics, since it applies to the saturation of parametric decay instabilities, nonlinear collisions of large–amplitude wave packets, radio frequency heating, and laser–plasma interactions [2, 3, 4]. In the domain of nonlinear optics, TWRI describes parametric amplification, frequency conversion, stimulated Raman and Brillouin scattering [5, 6, 7]. TWRIs have also been studied in the context of interactions of water waves [8, 9], interactions of bulk acoustic waves, surface acoustic waves [10] and wave–wave scattering in solid state physics. The physical model describing TWRI is completely integrable [11]. Integrability gives us mathematical tools to investigate several problems such as the evolution of given initial physical data by exploiting spectral methods [12, 13], and the existence of particular analytic solutions (f.i. solitons) [14, 15]. Soliton solutions are of particular interest in various nonlinear environments: from sound waves and charge–density waves to matter waves and electromagnetic waves [16, 17]. In spite of the large diversity of the systems in which soliton exist, the basic properties of solitons always follow the same trends [18]. The most fascinating feautures of solitons are their particle–like interaction phenomena [19, 20], and the interactions between solitons can result in soliton fusion, fission and annihilation, spiralling, breakup and so on. Here we present the TWRI dynamics of two input wave packets at frequency ω1, ω2 which mix to generate a field at the sum frequency ω3. Depending on the input intensities, three different regimes exist. Linear regime: the wave packets