Furthermore, in the polarized case, the integrand appearing on the left-hand side of Equation (58) is unbounded as . In fact, the best bound for the integrand is due to Equation (52). On the other hand, the integral is conserved. Moreover, since this conserved quantity determines the overall behavior of the solution, it is clear that the problem of analyzing the asymptotics numerically is not trivial. The same phenomenon appears in the nonpolarized case. However, it is of interest to note that the reason why the mathematical analysis is possible is in part due to the difference in decay rates between and
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