Acoustic scattering by a finite plate with a poroelastic extension using the unified transform method

2021 ◽  
pp. 116677
Author(s):  
Qian Liu ◽  
Yu Liu ◽  
Hanbo Jiang ◽  
Yannian Yang ◽  
Peng Zhou
Keyword(s):  
Acoustic Scattering ◽  
Transform Method ◽  
Finite Plate ◽  
Unified Transform Method

scholarly journals Solving PDEs of fractional order using the unified transform method

2018 ◽  
Vol 339 ◽  
pp. 738-749 ◽  
Author(s):  
Arran Fernandez ◽  
Dumitru Baleanu ◽  
Athanassios S. Fokas
Keyword(s):  
Fractional Order ◽  
Transform Method ◽  
Unified Transform Method

scholarly journals The unified transform method for the Sasa–Satsuma equation on the half-line

2013 ◽  
Vol 469 (2159) ◽  
pp. 20130068 ◽  
Author(s):  
Jian Xu ◽  
Engui Fan
Keyword(s):  
Boundary Value ◽  
Initial Boundary ◽  
Half Line ◽  
Transform Method ◽  
Global Relation ◽  
Unified Transform Method ◽  
Initial Boundary Value ◽  
Dirichlet To Neumann Map

We implement the unified transform method to the initial-boundary value (IBV) problem of the Sasa–Satsuma equation on the half line. In addition to presenting the basic Riemann–Hilbert formalism, which linearizes this IBV problem, we also analyse the associated general Dirichlet to Neumann map using the so-called global relation.

scholarly journals Solving Wiener–Hopf problems without kernel factorization

2014 ◽  
Vol 470 (2170) ◽  
pp. 20140304 ◽  
Author(s):  
Darren G. Crowdy ◽  
Elena Luca
Keyword(s):  
Fluid Mechanics ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Kernel Functions ◽  
New Method ◽  
Transform Method ◽  
New Approach ◽  
Mathematical Ideas ◽  
Analytical Functions ◽  
Unified Transform Method

A new approach to solving problems of Wiener–Hopf type is expounded by showing its implementation in two concrete and typical examples from fluid mechanics. The new method adapts mathematical ideas underlying the so-called unified transform method due to A. S. Fokas and collaborators in recent years. The method has the key advantage of avoiding what is usually the most challenging part of the usual Wiener–Hopf approach: the factorization of kernel functions into sectionally analytical functions. Two example boundary value problems, involving both harmonic and biharmonic fields, are solved in detail. The approach leads to fast and accurate schemes for evaluation of the solutions.

Fokas’s Unified Transform Method for linear systems

2017 ◽  
Vol 76 (3) ◽  
pp. 463-488 ◽  
Author(s):  
Bernard Deconinck ◽  
Qi Guo ◽  
Eli Shlizerman ◽  
Vishal Vasan
Keyword(s):  
Linear Systems ◽  
Transform Method ◽  
Unified Transform Method

Acoustic scattering from a finite plate: Generation of guided Lamb wavesS0,A0andA

2012 ◽  
Vol 131 (6) ◽  
pp. 4233-4242 ◽  
Author(s):  
N. Cité ◽  
F. Chati ◽  
D. Décultot ◽  
F. Léon ◽  
G. Maze
Keyword(s):  
Acoustic Scattering ◽  
Finite Plate
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