Download e-book for iPad: An introduction to nonharmonic Fourier series by Robert M. Young

By Robert M. Young

ISBN-10: 0080874096

ISBN-13: 9780080874098

ISBN-10: 0127728503

ISBN-13: 9780127728506

An advent to Non-Harmonic Fourier sequence, Revised version is an replace of a well-known and hugely revered vintage textbook. during the booklet, fabric has additionally been extra on fresh advancements, together with balance concept, the body radius, and purposes to sign research and the keep watch over of partial differential equations.

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3 Multidimensional optical solitons All the above examples of nonlinear periodic heterogeneous systems supporting stable solitons are one-dimensional. Multidimensional systems which may be included into the same general class were found too. An essential example is a model of a bulk medium composed of alternating layers with self-focusing and self-defocusing Kerr nonlinearity [165], which may be regarded as a multidimensional counterpart of NLM systems. Stable 2D cylindrical solitons were found in this model, both in the numerical form and by means of VA, which implies that the periodic alternation of the self-focusing and self-defocusing suppresses the instability against collapse.

A parabolic phase profile across the pulse, with a real coefficient b in front of it: •«ansatz(z, T) = A{z) sech f — - j exp [i(t){z) + ib{z)T^] . 6) All the free parameters in the ansatz are allowed to be functions of the evolutional variable z, the first objective being to derive a system of evolution equations for them. This is done using the fact that the NLS equation can be derived, in the form of 5S/6u* = 0, from the action functional S{u,u*}, where 6/5u* is the symbol for the variational derivative.

3: The phase diagram in the parametric plane i£,E^) for solitons in Eq. 5). The filled and unfilled rectangles correspond, respectively, to stable and splitting solitons. The most essential difference between the assumptions on which the VA was based and numerical results is that the fundamental mode of the soliton destruction under the action of the sinusoidally modulated dispersion is not decay into radiation, but splitting of the soliton into two apparently stable secondary solitons (which is accompanied by emission of a considerable amount of radiation).

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An introduction to nonharmonic Fourier series by Robert M. Young

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