On Numerical Solutions for a Class of Relativistic Quasilinear Schrödinger Equations

We study the numerical solutions for a class of quasilinear Schr & ouml;dinger equations arising from the self-channeling of high-power ultra short lasers in matter, which are associated with energy functionals with nonlinear principle parts so that the classical algorithm cannot directly be used. By the method of variable replacement to transform the quasilinear Schr & ouml;dinger equation into an semilinear elliptic equation, the numerical mountain pass algorithm is then applied. Some numerical experiments are also performed, including zero potential, nonzero constant potential and singular problem.