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Symmetric solutions to a modified nonlinear Schrödinger equation

This paper is concerned with constructing various types of symmetric solutions for the modified nonlinear Schrödinger equations which have appeared as several models in mathematical physics. We give a theoretic approach to deal with multi-bump type soliton solutions whose bumps exhibit symmetric patterns and whose energies are sums of the energies of solitons to some limiting problems. Our methods can handle various types of symmetric domains such as annular domains, spheres and spherical cylinders.