Numerical computation of an Evans function for travelling waves

We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller–Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed c≥sqrt(2δ) in the F-KPP equation.

Obverse side of tombstone of Jeanette Molling (possibly Arthur Molling); Strangriede Cemetery; Hannover Cemeteries Tombs

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Tombstone of Arthur Molling; Strangriede Cemetery (R 26.05); Hannover Cemeteries Tombs

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Detail of tombstone of Arthur Molling; Strangriede Cemetery (R 26.05); Hannover Cemeteries Tombs

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Obverse side of tombstone of Jeanette Molling (possibly Arthur Molling); Strangriede Cemetery; Hannover Cemeteries Tombs

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Arthur Liebert, Albert Einstein, Franz Oppenheimer, Mrs. Kurt Goldstein, Fritz Medicus and Arthur Liebert's son walking outside the Grand Hotel Curhaus during the Davoser Hochschulkurse; Davos, Switzerland Portraits Groups

The Davoser Hochschulkurse took place for the first time in 1928. Mainly university teachers from Germany, France, Switzerland (perhaps elsewhere) offered lectures to students recovering from tuberculosis at the health resort in the Swiss mountains. The lecturers were accommodated at the Grand Hotel Curhaus, where the lectures also took place.

Lucien Levy-Bruehl, Albert Einstein, Franz Oppenheimer, Arthur Liebert and his son, Paul Tillich, unidentified woman and Mrs. Charles Blondel outside the Grand Hotel Curhaus during the Davoser Hochschulkurse; Davos, Switzerland Portraits Groups

The Davoser Hochschulkurse took place for the first time in 1928. Mainly university teachers from Germany, France, Switzerland (perhaps elsewhere) offered lectures to students recovering from tuberculosis at the health resort in the Swiss mountains. The lecturers were accommodated at the Grand Hotel Curhaus, where the lectures also took place.

Portrait of the artist Arthur Segal Portraits Men

Born Iasi Romania July 13, 1875, died London 1944

Portrait of the artist Arthur Segal Portraits Men

Born Iasi Romania July 13, 1875, died London 1944

The artist Arthur Segal with his work; London Portraits Men

Born Iasi Romania July 13, 1875, died London 1944

Portrait of Arthur Neustadt.

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Studio portrait of unidentified Levy brother (most likely Arthur or Hermann) in military uniform; Nogent-Sur-Seine, France.

Photographer's imprint lower left corner

Portrait of Arthur Segal Portraits Men

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Arthur Segal Portraits Men

Dedication by Arthur Segal: Anneliese u. Niko Braun in herzlichster Liebe und Freundschaft. Arthur Segal. Juni 1924

Obverse side of tombstone of Jeanette Molling (possibly Arthur Molling); Strangriede Cemetery; Hannover Cemeteries Tombs

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