Spin Wave Breathers in ³He B

Abstract

We have already reported elsewhere [1] a short study of the following problems: the solution of the double sine-Gordon equations [2,3,4]

$$ \mathop {\text{u}}\nolimits_{\text{xx}} - \mathop {\text{u}}\nolimits_{\text{tt}} \text{ = }\; \mp \;(\sin {\text{u}} + \frac{1} {2}\lambda {\text{sin}}\frac{1} {2}{\text{u}}) $$

(1)

for boundary conditions u → c, u_X,u_XX, etc → 0, as |x| → ∞ and initial data u(x,0) = c; u_t(x,0) = a , |x| < l, u_t(x,0) = 0, |x| > l. The number c is a particular chosen zero of sinu+1/2λsin1/2u.¹ Most of the paper [1] was concerned with the case -ve sign and λ=1. We study this same problem again in the present paper, but we report additional results which provide a more comprehensive view of the behaviour of equations (1) under their chosen boundary conditions. Especially we are concerned with the creation and behaviour of breather solutions.