Membrane Solitons as Solitary Waves of Non-Linear Strings Dynamics

TL;DR

This paper constructs solutions to membrane theory equations, revealing that certain reductions lead to integrable systems with solitonic solutions and connections to nonlinear Schrödinger equations.

Contribution

It demonstrates the existence of solitonic solutions in membrane theory and shows their relation to integrable systems and nonlinear Schrödinger equations.

Findings

Existence of solitary wave solutions in membrane equations

Evidence of integrability in the reduced equations

Connection to nonlinear Schrödinger equations

Abstract

Families of solutions to the field equations of the covariant BRST invariant effective action of the membrane theory are constructed. The equations are discussed in a double dimensional reduction, they lead to a nonlinear equation for a one dimensional extended object. One family of solutions of these equations are solitary waves with several properties of solitonic solutions in integrable systems, giving evidence that in this double dimensional reduction the nonlinear equations are an integrable system. The other family of solutions found, exploits the property that the non linear system under some assumptions is equivalent to a non linear Schr$\ddot {o}$dinger equation.