Abstract
Solutions of the equation
where α is a scalar function of space coordinates are known as Beltrami fields and are of fundamental importance in different branches of modern physics (see, e.g., [128], [82], [43], [125], [4], [55], [50], [67]). For simplicity, here we consider the real-valued proportionality factor α. and real-valued solutions of (9.1), though the presented approach is applicable in a complex-valued situation as well (instead of complex Vekua equations their bicomplex generalizations should be considered, see Section 14.3). We consider equation (9.1) on a plane of the variables x and y, that is α and \( \overrightarrow B \) are functions of two Cartesian variables only. In this case, as we show in Section 9.2, equation (9.1) reduces to the equation
.
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© 2009 Birkhäuser Verlag AG
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(2009). Beltrami Fields. In: Applied Pseudoanalytic Function Theory. Frontiers in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0004-0_9
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DOI: https://doi.org/10.1007/978-3-0346-0004-0_9
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0003-3
Online ISBN: 978-3-0346-0004-0
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