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Titlebook: Mathematics of Wave Phenomena; Willy Dörfler,Marlis Hochbruck,Birgit Schörkhuber Conference proceedings 2020 Springer Nature Switzerland A

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Janina Gärtner,Wolfgang Reichel dipole interaction. On the other hand, we propose the use of an external substrate potential at the bottom of the lattice that mimics the substrate potential of a crystal. Thus, the results obtained in the experimental setup can be extrapolated to other systems described by this equation.
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Nobu Kishimoto,Yoshio Tsutsumianalytically approximate its shape. The interactions of kinks and antikinks is studied by using a numerical method, the Strauss–Vázquez,which is a conservative, finite difference scheme. This numerical method is second-order accurate in both space and time, and nonlinearly stable, exactly conserving
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Renato Lucàation experiments with powerful, vortex-carrying Bessel beams, where they act as attractors in the beam propagation dynamics. Nonlinear Bessel vortex beams provide indeed a new solution to the question of the stable propagation of ring-shaped vortex light beams in homogeneous self-focusing Kerr medi
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Valery Serovhe independent electric variable), in terms of invariants of the independent kinematic and electric variables. In the final section of the chapter we consider the linear specialization of the general nonlinear theory and discuss briefly the linear theory of piezoelectricity.
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Error Analysis of Discontinuous Galerkin Discretizations of a Class of Linear Wave-type Problems,his class includes important examples such as Maxwell’s equations and wave equations. We prove an optimal error bound which holds under suitable regularity assumptions on the solution. Our analysis is performed in a framework of evolution equations on a Hilbert space and thus allows for the combination with various time integration schemes.
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