On universality of critical behaviour in the focusing nonlinear
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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, 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 .
منابع مشابه
On universality of critical behaviour in the focusing
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.
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تاریخ انتشار 2008