Results 91 to 100 of about 1,222,314 (174)

Resurgent methods and the first Painlevé equation

, 2015
The paper is and extended form of a course given at a CIMPA master class held in LIMA, Perù, in the summer of 2008. It aims at showing the resurgent methods acting on an example and, along that line, to extend the presentation of the resurgence theory of
Delabaere, Eric
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Rational Solutions for the (2+1)-Dimensional Modified KdV-CBS Equation

Advances in Mathematical Physics, 2019
In this paper, with the help of symbolic computation, three types of rational solutions for the (2+1)-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation are derived.
Yan Li, Temuer Chaolu, Yuexing Bai
doaj   +1 more source

An Analysis of the Lie Symmetry and Conservation Law of a Variable-Coefficient Generalized Calogero–Bogoyavlenskii–Schiff Equation in Nonlinear Optics and Plasma Physics

Mathematics
In this paper, the symmetries and conservation laws of a variable-coefficient generalized Calogero–Bogoyavlenskii–Schiff (vcGCBS) equation are investigated by modeling the propagation of long waves in nonlinear optics, fluid dynamics, and plasma physics.
Shu Miao, Zi-Yi Yin, Zi-Rui Li, Chen-Yang Pan, Guang-Mei Wei   +4 more
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Asymptotics for the Sasa–Satsuma equation in terms of a modified Painlevé II transcendent

, 2019
We consider the initial-value problem for the Sasa–Satsuma equation on the line with decaying initial data. Using a Riemann–Hilbert formulation and steepest descent arguments, we compute the long-time asymptotics of the solution in the sector |x|≤Mt1/3 ...
Huang, L., Lenells, Jonatan,
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Classification of Real Solutions of the Fourth Painlevé Equation

Mathematics
Painlevé transcendents are usually considered as complex functions of a complex variable, but, in applications, it is often the real cases that are of interest.
Jeremy Schiff, Michael Twiton
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Painlevé analysis of the damped, driven nonlinear Schrödinger equation

, 1988
SynopsisIn this paper we apply the Painlevé tests to the damped, driven nonlinear Schrödinger equationwhere a(x, t) and b(x, t) are analytic functions of x and t, todetermine under what conditions the equation might be completely integrable.
Peter A. Clarkson
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Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy

Symmetry, Integrability and Geometry: Methods and Applications, 2006
We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with respect to these ...
Andrei K. Svinin
doaj  

Analytic Investigation of a Generalized Variable-Coefficient KdV Equation with External-Force Term

Mathematics
This paper investigates integrable properties of a generalized variable-coefficient Korteweg–de Vries (gvcKdV) equation incorporating dissipation, inhomogeneous media, and an external-force term.
Gongxun Li, Zhiyan Wang, Ke Wang, Nianqin Jiang, Guangmei Wei   +4 more
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A Lax Formalism for the Elliptic Difference Painlevé Equation

Symmetry, Integrability and Geometry: Methods and Applications, 2009
A Lax formalism for the elliptic Painlevé equation is presented. The construction is based on the geometry of the curves on P^1 × P^1 and described in terms of the point configurations.
Yasuhiko Yamada
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Solutions to an autonomous discrete KdV equation via Painlevé-type ordinary difference equations

Hirota’s discrete Korteweg–de Vries (KdV) equation is a well-known integrable two-dimensional partial difference equation regarded as a discrete analogue of the KdV equation.
Nobutaka Nakazono
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