Actually, in general dimension n ≥ 2, the magnetic field B is a 2-form where Bi,j = ∂jAk − ∂kAj ; in the case n = 3, B = curlA. The function U : R → R represents an electric potential. In the sequel, for the sake of simplicity, we limit ourselves to the particular case in which f(x, t) = K(x)|t|t, with p > 1 if n = 2 and 1 < p < n+2 n−2 if n ≥ 3. It is now well known that the nonlinear Schrödin...

With an extended mapping approach and a linear variable separation approach, a series of solutions (including the Weierstrass elliptic function solutions, solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived. Based on the derived solutions and using some multi-valued functions, we find ...

The accurate numerical simulation of wave disturbance within harbours requires consideration of both nonlinear and dispersive wave processes in order to capture such physical effects as wave refraction and diffraction, and nonlinear wave interactions such as the generation of harmonic waves. The Boussinesq equations are the simplest class of mathematical model that contain all these effects in ...

ABSTRACT In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric ...

We consider the long time behavior of solutions of the d-dimensional linear Boltzmann equation that arises in the weak coupling limit for the Schrödinger equation with a time-dependent random potential. We show that the intermediate mesoscopic time limit satisfies a Fokker-Planck type equation with the wave vector performing a Brownian motion on the (d − 1)-dimensional sphere of constant energy...

We establish a long time soliton asymptotics for a nonlinear system of Maxwell equation coupled to a charged particle. The coupled system has a six dimensional manifold of soliton solutions. We show that in the large time approximation, any solution, with an initial state close to the solitary manifold, is a sum of a soliton and a dispersive wave which is a solution of the free Maxwell equation...

The current work handles for the first time, dispersive optical solitons in fiber Bragg gratings nonlinear (2+1)-dimensional Kundu–Mukherjee–Naskar equation. Two integration schemes, namely, modified Kudryashov’s approach and addendum to methodology are applied. Dark bright soliton solutions as long explicit obtained. Also, combo bright-singular introduced.

The generalized channel Boussinesq (gcB) two-equation model and the forced channel Kortewegae Vries (cKdV) one-equation model previously derived by the authors are further analysed and discussed in the present study. The gcB model describes the propagation and generation of weakly nonlinear, weakly dispersive and weakly forced long water waves in channels of arbitrary shape that may vary both i...