Properties of solitary wave solutions to the nonlinear Dirac-Klein-Gordon equation (Q1080076)

Solitary waves \(\psi (\xi)=e^{ia\xi} \phi (\xi)\), where \(\xi =x-ut\), \(\phi(\xi)\) is real, to the Euler-Lagrange equation \[ ik \psi_ t+i\mu \psi x+D \psi_{xx}-K \psi_{tt}-A_ 2 \psi -A_ 4 | \psi |^ 2 \psi = 0 \] are dealt with. The authors investigate dependence of the energy corresponding to this solution on the velocity \(u\) and give the limiting conditions on \(u\).