Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

Abstract

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2σ+1. These solutions collapse with the quasi self-similar ring profile, with ring width L(t) that vanishes at singularity, and radius proportional to L^α, where α=(4-σ)/(σ(d-1)). The blowup rate of these solutions is 1/(3+α) for 4/d\leσ<4, and slightly faster than 1/4 for σ=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.

21 pages, 13 figures, research article

References in corpus (3)

• Singular solutions of the L^2-supercritical biharmonic Nonlinear Schrodinger equation
• Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation
• Singular standing-ring solutions of nonlinear partial differential equations

Cited by in corpus (8)

• Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
• Singular solutions of the L^2-supercritical biharmonic Nonlinear Schrodinger equation
• Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation
• Singular standing-ring solutions of nonlinear partial differential equations
• Dynamics of solutions in the 1d bi-harmonic nonlinear Schrödinger equation
• Solving the nonlinear biharmonic equation by the Laplace-Adomian and Adomian Decomposition Methods
• Blowup of cylindrically symmetric solutions for biharmonic NLS
• A discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations