On universality of critical behaviour in the focusing
نویسندگان
چکیده
We argue that the critical behaviour near the point of " gradient catastrophe " of the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation ii ψ t + 2 2 ψ xx + |ψ| 2 ψ = 0 with analytic initial data of the form ψ(x, 0;) = A(x) e i S(x) is approximately described by a particular solution to the Painlevé-I equation.
منابع مشابه
On universality of critical behaviour in the focusing nonlinear
We argue that the critical behaviour near the point of " gradient catastrophe " of the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation ii Ψ t + 2 2 Ψ xx + |Ψ| 2 Ψ = 0, 1, with analytic initial data of the form Ψ(x, 0;) = A(x) e i S(x) is approximately described by a particular solution to the Painlevé-I equation .
متن کاملNumerical Investigation of Rail Bending Behaviour Focusing on the Effect of Track Modulus
Thorough understanding of steel rail response to wheel load is a key step towards design and evaluation of the railway track structure. In current practice, maximum vertical deflection and bending moment are calculated using the theory of infinite beam on continuous elastic foundation (Winkler model), in which the foundation stiffness is assumed as constant. However, variation of track modulus ...
متن کاملUniversality of global dynamics for the cubic wave equation
We consider the initial value problem for the spherically symmetric, focusing cubic wave equation in three spatial dimensions. We give numerical and analytical evidence for the existence of a universal attractor which encompasses both global and blowup solutions. As a byproduct we get an explicit description of the critical behaviour at the threshold of blowup. Mathematics Subject Classificatio...
متن کاملIntroduction to Schramm-Loewner evolution and its application to critical systems
In this short review we look at recent advances in Schramm-Loewner Evolution (SLE) theory and its application to critical phenomena. The application of SLE goes beyond critical systems to other time dependent, scale invariant phenomena such as turbulence, sand-piles and watersheds. Through the use of SLE, the evolution of conformally invariant paths on the complex plane can be followed; hence a...
متن کاملThe progress mechanism of track geometrical irregularity focusing on hanging sleepers
This topic is very traditional and basically has been concerned for a long time. A lot of sophisticated vehicle/track interaction model and track dynamic deterioration model have been developed so far. The author also developed a track settlement progress model comprising a vehicle/track interaction model and a track settlement law. Hanging sleepers are usually caused more or less by the dyn...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009