Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection

Abstract

In this work we continue the description of soliton-like solutions of some slowly varying, subcritical gKdV equations. In this opportunity we describe, almost completely, the allowed behaviors: either the soliton is refracted, or it is reflected by the potential, depending on its initial energy. This last result describes a new type of soliton-like solution for gKdV equations, also present in the NLS case. Moreover, we prove that the solution is not pure at infinity, unlike the standard gKdV soliton.

51 pages, submitted

References in corpus (5)

• Solitary Wave Dynamics in an External Potential
• Fast soliton scattering by delta impurities
• Soliton splitting by external delta potentials
• Long time motion of NLS solitary waves in a confining potential
• Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves

Cited by in corpus (1)

• Inelastic character of solitons of slowly varying gKdV equations