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Bifurcation revisited along footprints of Jürgen Scheurle

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  • Actual research concerning, in particular, the occurrence of "gap-solitons" bifurcating from the continuous spectrum confirms that this part of Bifurcation Theory that started around 40 years ago flourishes. In this lecture we review the origins of "Bifurcation from the continuous spectrum" with regard to the achievements of Jürgen Scheurle and sketch how the early results dealing with the bifurcation of singular solutions have prepared the ground for present and further developments.

    Mathematics Subject Classification: Primary: 34C23, 37G99; Secondary: 35J20, 47E05.


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  • Figure 1.  Phase portrait for $ \lambda >0 $

    Figure 2.  Heteroclinic orbit (singular solution)

    Figure 3.  (a) λ > 0, (b) λ < 0

    Figure 4.  Prof. Tassilo Küpper and Prof. Jürgen Scheurle

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