We consider the asymptotic behavior of solutions to nonlinear partial differential equations in the limit of short wavelength. For initial data which cause focusing at one point, we highlight critical indexes as far as the influence of the nonlinearity in the neighborhood of the caustic is concerned. Our results generalize some previous ones proved by the first author in the case of nonlinear S...

We propose nonlinear integral equations to describe the groundstate energy of the fractional supersymmetric sine-Gordonmodels. The equations encompass theN = 1 supersymmetric sine-Gordonmodel as well as the φid,id,adj perturbation of the SU(2)L×SU(2)K/SU(2)L+K models at rational level K. A second set of equations are proposed for the groundstate energy of the N = 2 supersymmetric sine-Gordon mo...

In this report, we study various nonlinear wave equations arising in mathematical physics and investigate the existence of solutions to these equations using variational methods. In particular, we look for particle-like traveling wave solutions known as solitary waves. This study is motivated by the prevalence of solitary waves in applications and the rich mathematical structure of the nonlinea...