The interaction between sound and ultrasound waves in a weakly compressible viscous liquid with gas bubbles is considered. Using the method of multiple scales oneand two-dimensional nonlinear interaction equations are derived. The degeneracy of the interaction is found in bubbly fluids. This phenomenon lies in the fact that the interaction coefficients vanish at a certain frequency of ultrasoun...

We present new solutions in terms of elementary functions of the multi-component nonlinear Schrödinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. ...

This paper is devoted to the classification of integrable Davey-Stewartson type equations. A list of potentially deformable dispersionless systems is obtained through the requirement that such systems must be generated by a polynomial dispersionless Lax pair. A perturbative approach based on the method of hydrodynamic reductions is employed to recover the integrable systems along with their Lax...

The possibility of finite-time, dispersive blow up for nonlinear equations of Schrödinger type is revisited. This mathematical phenomena is one of the possible explanations for oceanic and optical rogue waves. In dimension one, the possibility of dispersive blow up for nonlinear Schrödinger equations already appears in [9]. In the present work, the existing results are extended in several ways....