The heteroclinic connection problem for general double-well potentials

Abstract

By variational methods, we provide a simple proof of existence of a heteroclinic orbit to the Hamiltonian system $u^{\prime \prime }=\nabla W(u)$ that connects the two global minima of a double-well potential $W$. Moreover, we consider several inhomogeneous extensions.

this version contains some more recent references compared to the published one, Mediterranean Journal of Mathematics (2016)

References in corpus (4)

• Domain walls in the coupled Gross-Pitaevskii equations
• Phase coexistence in consolidating porous media
• Phase segregation for binary mixtures of Bose-Einstein Condensates
• On the connection problem for the p-Laplacian system for potentials with several global minima

Cited by in corpus (7)

• Existence of periodic orbits near heteroclinic connections
• Energy estimates for minimizers to a class of elliptic systems of Allen-Cahn type and the Liouville property
• On the existence of connecting orbits for critical values of the energy
• A DeGiorgi type conjecture for minimal solutions to a nonlinear Stokes equation
• Layered solutions to the vector Allen-Cahn equation in $R^2$. Characterization of minimizers and a new approach to heteroclinic connections
• On the existence of dark solitons of the cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity
• A necessary condition in a De Giorgi type conjecture for elliptic systems in infinite strips