Airy and Painlevé asymptotics for the mKdV equation
نویسندگان
چکیده
منابع مشابه
On Asymptotics for the Airy Process
The Airy process t → A(t), introduced by Prähofer and Spohn, is the limiting stationary process for a polynuclear growth model. Adler and van Moerbeke found a PDE in the variables s1, s2 and t for the probability Pr (A(0) ≤ s1, A(t) ≤ s2). Using this they were able, assuming the truth of a certain conjecture and appropriate uniformity, to obtain the first few terms of an asymptotic expansion fo...
متن کامل3 Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlevé Equation . I
The degenerate third Painlevé equation, u= (u ) u −u′ τ + τ (−8εu2+2ab)+b2 u , where ε, b∈R, and a∈C, and the associated tau-function are studied via the Isomonodromy Deformation Method. Connection formulae for asymptotics of the general as τ→±0 and ±i0 solution and general regular as τ→±∞ and ±i∞ solution are obtained. 2000 Mathematics Subject Classification. 33E17, 34M40, 34M50, 34M55, 34M60 ...
متن کاملOn the asymptotics of the real solutions to the general sixth Painlevé equation
The mathematical and physical significance of the six Painlevé transcendents has been well established. In the last 20 to 30 years, many mathematicians have spent dramatic effort on studying the properties of these transcendents. Although it is the most complicated one among the six Painlevé equations, there have been many results about the sixth Painlevé transcendent. In fact, the asymptotics ...
متن کاملAuxiliary equation method for the mKdV equation with variable coefficients
By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of nonlinear evolution equations with variable coefficients. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, new explicit solutions including solitary wave solutions and trigonometric function solutions...
متن کاملAsymptotics for the Covariance of the Airy 2 Process
In this paper we compute some of the higher order terms in the asymptotic behavior of the two point function P(A2(0)≤ s1,A2(t)≤ s2), extending the previous work of Adler and van Moerbeke (arXiv:math.PR/0302329; Ann. Probab. 33, 1326–1361, 2005) and Widom (J. Stat. Phys. 115, 1129–1134, 2004). We prove that it is possible to represent any order asymptotic approximation as a polynomial and integr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2019
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12265