Solutions of $x''=t^{\alpha\lambda-2}x^{1+\alpha}$ with Movable Singularity

Generalized Solutions Describing Singularity Interaction

Periodic Solutions of Damped Duffing-type Equations with Singularity

We consider a second order equation of Duffing type. By applying Mawhin’s continuation theorem and a relationship between the periodic and the Dirichlet boundary value problems for second order ordinary differential equations, we prove that the given equation has at least one positive periodic solution when the singular forces exhibits certain some strong force condition near the origin and wit...

Singularity-free Cosmological Solutions in String Theories

Singularity-free cosmological solutions may be obtained from the string action at tree level if the dimension of the space-time is greater than 10 and if brane configurations are taken into account. The behaviour of the dilaton field in this case is also regular. Asymptotically a radiative phase is attained indicating a smooth transition to the standard cosmological model. PACS number(s): 04.20...

Self-similar Solutions of the Localized Induction Approximation: Singularity Formation

Exact solutions of nonlinear partial differential equations by singularity analysis

Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with essentially the same toolbox, when one looks for analytic solutions in closed form. The basic tool is the appropriate use of the singularities of the solutions, and this can be done without knowing these solutions in advance. Since the elaboration of the si...