Finite-time Singularities in Coupled Nonlinear Schrodinger Equations with 4-Wave Mixing
Student Ben Safdi
Dates of Involvement 2007
Faculty Advisor Harvey Segur
I work with Harvey Segur in finding new singular solutions in coupled nonlinear Schrodinger (NLS) equations with 4-wave mixing. Unlike previous singularities in NLS systems, ours do no imply spatial collapse but rather unbounded growth in wave amplitudes, with no spatial variation. Moreover, a boundary is found in coefficient space such that singular solutions are guaranteed if the coefficients of the nonlinear terms satisfy a certain inequality and sign rule. With no spatial variation, the coupled partial differential equations reduce to ordinary differential equations (ODEs). Then the condition on the coefficients allows an explicit general solution of the ODEs. The singularities are unavoidable and found to occur for all values of the Hamiltonian.
About Ben Safdi:
Ben Safdi was born on April 19 1986 in Cincinnati, Ohio. He attended Seven Hills middle and upper school, where he discovered a passion of physics and mathematics. Upon graduation he enrolled in the University of Colorado at Boulder school of engineering. He is currently a junior double majoring in engineering physics and applied mathematics with a minor in Japanese. In addition to his MCTP research, Ben is an undergraduate research assistant at JILA working in Jun Ye’s lab for AMO physics and precision measurement. Outside of classes, he enjoys rock climbing, which he competes in on the professional level with sponsors including FiveTen.
