Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solut...

In this paper, we employ the modified simple equation method to find the exact traveling wave solutions involving parameters of nonlinear evolution equations via the (1+1)dimensional generalized shallow water-wave equation and the(2+1)-dimensional KdV-Burgers equation. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave sol...

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function ...

These lectures deal with the description of hadronic scattering at high energies, and more specifically with the evolution of the scattering matrix with energy[1],[2]. It has been a very lively and active field for the last 10 years[3],[4],[5],[6] and especially lately there has been a new burst of activity. The latest developments are related to what is sometimes called Pomeron loops[7], or Fl...

These lectures deal with the description of hadronic scattering at high energies, and more specifically with the evolution of the scattering matrix with energy[1],[2],[3]. It has been a very lively and active field for the last 10 years[4],[5],[6],[7] and especially lately there has been a new burst of activity. The latest developments are related to what is sometimes called Pomeron loops[8], o...

An extended mapping method is used to drive some new exact travelling wave solutions of nonlinear evolution equations arising in physics,namely,generalized Hirota-Satsuma coupled KdV system and coupled Maccaris equations.As a result,many exact travelling wave solutions are obtained which include new solitary wave solutions,triangular and hyperbolic functions.Solutions in the limiting cases have...

In this paper,an extended mapping method with symbolic computation is developed to obtain new periodic wave solutions in terms of Jacobin elliptic function for nonlinear evolution equations arising in mathematical physics.As a result,many exact travelling wave solutions are obtained which include new solitary wave solutions,triangular and hyperbolic functions.Solutions in the limiting cases hav...

Wave fields traveling through a varying medium (e.g. topography, currents), can develop well-defined focal zones and caustics, where the wave field is highly coherent and wave statistics vary rapidly. However, the presence and evolution of such coherent structures in the wave field are not resolved in a quasi-homogeneous description of the wave field (e.g. the radiative transport equation), and...