Nonlinear chiral dispersive waves

Abstract

Whitham's theory of nonlinear water waves is applied to a classical field with the lagrangian density L=1/2((( delta ^mu phi )( delta _mu phi )-m² phi ²)/(1+ lambda phi ²)). This is the isoscalar analogue of a chiral invariant SU(2)(X)SU(2) lagrangian with symmetry breaking term included. The corresponding field equation admits simple harmonic plane-wave solutions. The author found that the important field quantities of these waves, namely the wavenumber k and amplitude A obey a system of first- order partial differential equations. When the coupling parameter lambda is negative in sign, the system is hyperbolic, which implies that any inhomogeneities in k and A propagate with certain (amplitude-dependent) velocities. These velocities, which are the nonlinear generalization of the group velocity in the Whitham sense, are calculated.