A plane wave propagating in a medium with focusing nonlinearity is unstable with respect to the generation of small scale filaments [1]. This so called modulational instability (MI) phenomenon, has been extensively studied because of its importance as a factor limiting the propagation of high power beams. Filamentation may also be identified as the first stage in the development of turbulent fl...

This study deals with the stochastic dynamic behaviors of nonlinear vibration of the fluid-conveying double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. Besides, the small scale effects of the nonlinear vibration of the DWCNTs are investigated by using the theory of nonlocal elasticity. Some statisti...

We study behavior of solutions to the nonlinear generalized Hartree equation, where nonlinearity is nonlocal type and expressed as a convolution iut+?u+(|x|?(N??)?|u|p)|u|p?2u=0,x?RN,t?R. Our main goal understand global this equation in various settings. In work we make an initial attempt towards H1 (finite energy) solutions. first investigate local well-posedness small data theory. then, inter...

An explanation is given for previous numerical results which suggest a certain bifurcation of ‘vector solitons’ from scalar (single-component) solitary waves in coupled nonlinear Schrödinger (NLS) systems. The bifurcation in question is nonlocal in the sense that the vector soliton does not have a small-amplitude component, but instead approaches a solitary wave of one component with two infini...