The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing along a curvilinear trajectory in inhomogeneous and nonlinear saturable media. CGO method reduces the problem of Gaussian beam propagation in inhomogeneous and nonlinear media to solving ordinary differential equations for the complex curvature of the wave front and for ...

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolu...

ABSTRACT Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modif...

Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlin...

Graviational radiation is described by canonical Yang-Mills wave equations on the curved space-time mani-fold, together with evolution equations for the metric in the tangent bundle. The initial data problem is described in Yang-Mills scalar and vector potentials, resulting in Lie-constraints in addition to the familiar Gauss-Codacci relations.

Graviational radiation is described by canonical YangMills wave equations on the curved space-time manifold, together with evolution equations for the metric in the tangent bundle. The initial data problem is described in Yang-Mills scalar and vector potentials, resulting in Lie-constraints in addition to the familiar Gauss-Codacci relations.

From the outset, mathematicians and physicists have been concerned with the ways in which solutions to this equation can be associated to classical particle motion, and the ways in which they cannot: the classical dynamical behavior of particles is intermixed with dispersive spreading and interference phenomena in quantum theory. More recently, nonlinear Schrödinger equations have come to play ...

Nonlinear evolution wave equations (NEEs) are partial differential equations (PDEs) involving first or second order derivatives with respect to time. Such equations have been intensively studied for the past few decades [1-3] and several new methods to solve nonlinear PDEs either numerically or analytically are now available. Hirota's bilinear method is a powerful tool for obtaining a wide clas...

This paper discusses the existence and stability of solitary-wave solutions of a general higher-order Benjamin-Bona-Mahony (BBM) equation, which involves pseudo-differential operators for the linear part. One of such equations can be derived from water-wave problems as second-order approximate equations from fully nonlinear governing equations. Under some conditions on the symbols of pseudo-dif...