Linear interaction analysis (LIA) is routinely used to study the shock–turbulence in supersonic and hypersonic flows. It based on inviscid of elementary Kovásznay modes with a shock discontinuity. LIA neglects nonlinear effects, hence it limited small-amplitude disturbances. In this work, we extend framework fundamental two-dimensional vorticity wave normal shock. The predictions from weakly ar...

The motivation for this work is the stability problem for short-crested Stokes waves. A new point of view is proposed, based on the observation that an understanding of the linear stability of short-crested waves (SCWs) is closely associated with an understanding of the stability of the oblique non-resonant interaction between two waves. The proposed approach is to embed the SCWs in a six-param...

The dependence of ENSO’s period on its amplitude is examined using a simple delayed oscillator model. This dependence is first calculated in the strongly nonlinear regime by extracting and analyzing unstable periodic orbits from the chaotic attractor of the model. In this regime, the period is found to decrease with increasing amplitude. Next, the dependence of the period on the amplitude is al...

In this paper we investigate the propagation of conical waves in nonlinear media. In particular, we are interested in the effects resulting from applying a Gaussian apodization to an ideal nondiffracting wave. First, we present a multiple scales approach to derive amplitude equations for weakly nonlinear conical waves from a governing equation of cubic nonlinear Schrödinger type. From these equ...

Many of nonlinear systems in the field of engineering such as nano-resonator and atomic force microscope can be modeled based on Duffing equation. Analytical frequency response of this system helps us analyze different interesting nonlinear behaviors appearing in its response due to its rich dynamics. In this paper, the general form of Duffing equation with cubic nonlinearity as well as par...