Singular solutions of the L^2-supercritical biharmonic Nonlinear Schrodinger equation

Abstract

We use asymptotic analysis and numerical simulations to study peak-type singular solutions of the supercritical biharmonic NLS. These solutions have a quartic-root blowup rate, and collapse with a quasi self-similar universal profile, which is a zero-Hamiltonian solution of a fourth-order nonlinear eigenvalue problem.

References in corpus (4)

• Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case
• Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation
• Singular standing-ring solutions of nonlinear partial differential equations
• Mass concentration for the $L^2$-critical Nonlinear Schrödinger equations of higher orders

Cited by in corpus (5)

• Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
• Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation
• Dynamics of solutions in the 1d bi-harmonic nonlinear Schrödinger equation
• Blowup of cylindrically symmetric solutions for biharmonic NLS
• Petviashvilli's Method for the Dirichlet Problem