TY - JOUR

T1 - Ring-type singular solutions of the biharmonic nonlinear Schrödinger equation

AU - Baruch, G.

AU - Fibich, G.

AU - Mandelbaum, E.

PY - 2010/11

Y1 - 2010/11

N2 - We present new singular solutions of the biharmonic nonlinear Schrödinger equation (NLS) it (t, x) - δ2 + ||2s = 0, x Rd , 4/d σ s σ 4. These solutions collapse with the quasi-self-similar ring profile QB , where QB (t, r)| ̃ 1 L2/s (t) QB σ r - rmax(t) L(t) δ , r= |x|, L(t) is the ring width that vanishes at singularity, rmax(t) ̃ r0La(t) is the ring radius, and a = (4 - s)/(s (d - 1)). The blowup rate of these solutions is 1/(3 + a) for 4/d σ s < 4, and slightly faster than 1/4 for s = 4. These solutions are analogous to the ring-type solutions of the NLS.

AB - We present new singular solutions of the biharmonic nonlinear Schrödinger equation (NLS) it (t, x) - δ2 + ||2s = 0, x Rd , 4/d σ s σ 4. These solutions collapse with the quasi-self-similar ring profile QB , where QB (t, r)| ̃ 1 L2/s (t) QB σ r - rmax(t) L(t) δ , r= |x|, L(t) is the ring width that vanishes at singularity, rmax(t) ̃ r0La(t) is the ring radius, and a = (4 - s)/(s (d - 1)). The blowup rate of these solutions is 1/(3 + a) for 4/d σ s < 4, and slightly faster than 1/4 for s = 4. These solutions are analogous to the ring-type solutions of the NLS.

UR - http://www.scopus.com/inward/record.url?scp=78149335261&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/23/11/008

DO - 10.1088/0951-7715/23/11/008

M3 - מאמר

AN - SCOPUS:78149335261

VL - 23

SP - 2867

EP - 2887

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 11

ER -