Detection of standing pulses in periodic media by pulse interaction
The paper addresses the nonlinear Klein-Gordon equation with spatially periodic coefficients \(a(x)\) and \(b(x)\) NEWLINE\[NEWLINE u_{tt} = u_{xx} -a(x)u + b(x)u^3. NEWLINE\]NEWLINE The objective is to study, by means of analytical methods, the dynamics of approximate soliton solutions in this model, especially collisions between quiescent and moving solitons. The analysis uses the Fourier transform of the field, then returning to the \(x\)-space. The main problem is the separation of the internal and external dynamics of the colliding solitons. It is suggested that the elaborated method may find applications to more general models of nonlinear disperive media with spatially periodic coefficients.
scientific article; zbMATH DE number 6071619
scientific article