K-dV Like Equations with Domain Wall Solutions and Their Hamiltonians

Abstract

We consider K-dV like equations with higher order nonlinearity and show that these have domain wall (kink) solutions for particular values of the coefficient of the nonlinear terms. The solutions are compared with the domain wall solutions of relativistic field theories. The exact Hamiltonian densities are also evaluated for these equations, using Dirac’s constrained Hamiltonian formalism. The conservation of the Hamiltonians is explained in terms of the contribution of the corresponding fields from spatial infinities.