Analytical construction of soliton families in one‐ and two‐dimensional nonlinear Schrödinger equations with nonparity‐time‐symmetric complex potentials [PDF]
Studies in applied mathematics (Cambridge), 2021 The existence of soliton families in nonparity‐time‐symmetric complex potentials remains poorly understood, especially in two spatial dimensions. In this article, we analytically investigate the bifurcation of soliton families from linear modes in one ...
Jianke Yang
semanticscholar +1 more source
A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics
Journal of elasticity, 2022 Introducing a crack in an elastic plate is challenging from the mathematical point of view and relevant within an engineering context of evaluating strength and reliability of structures. Accordingly, a multitude of associated works is available to date,
J. Scheel, D. Wallenta, A. Ricoeur
semanticscholar +1 more source
Machine learning potentials for complex aqueous systems made simple [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2021 Significance Understanding complex materials, in particular those with solid–liquid interfaces, such as water on surfaces or under confinement, is a key challenge for technological and scientific progress.
Christoph Schran +5 more
semanticscholar +1 more source
Sharp bounds for eigenvalues of biharmonic operators with complex potentials in low dimensions [PDF]
Mathematische Nachrichten, 2019 We derive sharp quantitative bounds for eigenvalues of biharmonic operators perturbed by complex‐valued potentials in dimensions one, two and three.
O. O. Ibrogimov +2 more
semanticscholar +1 more source
Journal of Mathematical Analysis and Applications, 1999 The authors show that complex potentials associated with locally sourceless and locally irrotational flows defined on (possibly infinitely connected) domains in the complex plane have logarithmic singularities. Additionally, some applications to flows around contours are given.
Boettger, Ulrich +2 more
openaire +1 more source
A New Approach to Non-Singular Plane Cracks Theory in Gradient Elasticity
Mathematical and Computational Applications, 2019 A non-local solution is obtained here in the theory of cracks, which depends on the scale parameter in the non-local theory of elasticity. The gradient solution is constructed as a regular solution of the inhomogeneous Helmholtz equation, where the ...
Sergey A. Lurie +2 more
doaj +1 more source
Trace formulas for Schrödinger operators with complex potentials on a half line [PDF]
Letters in Mathematical Physics, 2018 We consider Schrödinger operators with complex-valued decaying potentials on the half line. Such operator has essential spectrum on the half line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half line ...
E. Korotyaev
semanticscholar +1 more source
Late ventricular potentials in risk assessment of the occurrence of complex ventricular arrhythmia in patients with myocardial infarction and heart failure [PDF]
Vojnosanitetski Pregled, 2004 Aim. To determine the prognostic significance of late ventricular potentials on signal-averaged electrocardiogram and left ventricular ejection fraction for the occurrence of complex ventricular arrhythmia in patients treated with accelerated tissue-type
Ćosić Zoran +3 more
doaj +1 more source
Revisiting the Reflected Caustics Method: the Accurate Shape of the “Initial Curve”
Engineering Transactions, 2013 The shape of the “initial curve”, i.e. the locus of material points, which if properly illuminated provide (under specific conditions) the “caustic curve”, is explored.
Christos F. MARKIDES +1 more
doaj +1 more source
Analytically Solvable PT-Invariant Periodic Potentials [PDF]
, 2004 Associated Lam\'e potentials $V(x)=a(a+1)m\sn^2(x,m)+b(b+1)m{\cn^2 (x,m)}/{\dn^2(x,m)}$ are used to construct complex, PT-invariant, periodic potentials using the anti-isospectral transformation $x \to ix+\beta$, where $\beta$ is any nonzero real number.
Abramowitz +36 more
core +3 more sources