Superposition in nonlinear wave and evolution equations

As has been shown recently [Cooper et al. 2002], [Khare et al. 2002a], [Khare et al. 2003], [Khare et al. 2002b] (periodic) Jacobian elliptic functions (if they are solutions of a certain nonlinear wave and evolution equation (NLWEE)) are start solutions for generating new solutions of the NLWEE by a linear superposition procedure. Thus, elliptic functions are of specific importance for finding solutions of NLWEEs. On the other hand, based on a symmetry reduction method, a technique to obtain elliptic solutions of certain NLWEEs was proposed and applied to the gmKPE and the NLCQSE [Schürmann 1996], [Schürmann et al. 2004a], [Schürmann et al. 2004b]. Department of Physics, University of Osnabrück, D-49069 Osnabrück, Germany, corresponding author: [email protected]. Department of Mathematical Sciences, University of Oulu, FIN-90014 Finland.