The asymptotic theory of global solutions for semilinear wave equations in three space dimensions

Abstract

This paper deals with the asymptotic theory of initial value problems for semilinear wave equations in three space dimensions. The well posedness and validity of formal approximations about time T --c~ are discussed in the classical sense of C 2. The results describe the validity of formal global solutions. Using a time-scale perturbation method, an application of the asymptotic theory is given to analyze a special wave equation in three space dimensions. (~)

Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

“…where the parameters , can be found by balancing the highest-order linear term with the nonlinear terms in (11) and (15), respectively. In (11), we balance with V, to obtain +2 = + , and then = 2.…”

“…Kilicman and Abazari [10] used the ( / )-expansion method to construct periodic and soliton solutions for the Schrödinger-Boussinesq. The investigation of nonlinear partial differential equations plays an important role in the study of nonlinear physical phenomena [9][10][11][12].…”