The One Dimensional Focusing Nonlinear Schrödinger Equation and Their Regular Solutions
MathematicsWe consider the classical one-dimensional focusing nonlinear Schrödinger equation (NLS). We give a brief overview of the techniques used to solve it since its formulation. Then we present various results obtained by the author in recent years.
Pierre Gaillard
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On Asymptotic Behaviors of Acoustic Waves Due to High‐Contrast Material Inclusions
Studies in Applied Mathematics, Volume 154, Issue 4, April 2025.ABSTRACT This paper investigates the asymptotic behaviors of time‐harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high‐contrast material parameters. We derive sharp asymptotic estimates and obtain several effective acoustic obstacle scattering models when the material parameters take extreme ...
Yueguang Hu, Hongyu Liu
wiley +1 more source
Double Wronskian Representation of the Nth-Order Solutions to the Davey–Stewartson Equations
AxiomsSolutions to the Davey–Stewartson equations (DS) in terms of the determinants of order 2N depending on 4N real parameters are constructed. The Darboux transformation is used to construct solutions of order N to this equation.
Pierre Gaillard
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Wronskian formulation of the spectrum of curvature perturbations
Journal of Cosmology and Astroparticle Physics, 2006 13 pages, 1 figures, submitted to JCAP, Minor corrections have been ...
Yokoyama, S +3 more
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On the Growths of Meromorphic Function Generated Wronskians from the View Point of Slowly Changing Functions [PDF]
, 2015 In the paper we extend and sometimes improve few results on comparative growth properties of composite entire or meromorphic functions using m-th generalized {p}L*-order and the m-th generalized {p}L*-lower order and wronskians generated by one of the ...
Biswas, Tanmay +2 more
core
MathematicsThis article examines the integrability of the combined KdV-mKdV equation, which provides an effective framework for modeling coherent structures in turbulent flows.
Reem Abdullah Aljethi +3 more
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Some Approaches to Solving the KP Equation: Different Representations and Various Types of Solutions
AxiomsWe present different methods to construct solutions to the Kadomtsev–Petviashvili (KP) equation. In the first method, from the solutions to the NLS equation, we construct solutions to the KP equation in terms of Fredholm determinants. We deduce solutions
Pierre Gaillard
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Entanglement Renyi Entropy of Two Disjoint Intervals for Large c Liouville Field Theory. [PDF]
Entropy (Basel), 2022 Tsujimura J, Nambu Y.
europepmc +1 more source
On one generalization of Wronskian
Lietuvos matematikos rinkinys, 2007 In this article the properties of the specially introduced determinant, elements of which are the divideddifferences in different orders are studied. The close connection of this determinant with the Chebyshevsystem and the ordinary differential equation is indicated.
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Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations [PDF]
, 2013 We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations.
Clarkson, Peter
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